Chemical engineering education ( Journal Site )

Material Information

Chemical engineering education
Alternate Title:
Abbreviated Title:
Chem. eng. educ.
Physical Description:
v. : ill. ; 22-28 cm.
American Society for Engineering Education -- Chemical Engineering Division
Chemical Engineering Division, American Society for Engineering Education
Place of Publication:
Storrs, Conn
Publication Date:
annual[ former 1960-1961]


Subjects / Keywords:
Chemical engineering -- Study and teaching -- Periodicals   ( lcsh )
periodical   ( marcgt )
serial   ( sobekcm )


Chemical abstracts
Additional Physical Form:
Also issued online.
Dates or Sequential Designation:
1960-June 1964 ; v. 1, no. 1 (Oct. 1965)-
Numbering Peculiarities:
Publication suspended briefly: issue designated v. 1, no. 4 (June 1966) published Nov. 1967.
General Note:
Title from cover.
General Note:
Place of publication varies: Rochester, N.Y., 1965-1967; Gainesville, Fla., 1968-

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
oclc - 01151209
lccn - 70013732
issn - 0009-2479
lcc - TP165 .C18
ddc - 660/.2/071
System ID:

Full Text

chemial engineerg ed






2nd Edition
Richard M. Felder and Ronald W.
Rousseau, both of North Carolina State
Now expanded and improved at its second
edition, this widely acclaimed text covers a
large body of topics drawn from traditional
chemical process analysis, applied physical
chemistry, mathematical analysis and computer
applications. A superior Instructor's Manual in-
cludes transparency masters, a topic-problem
matrix, suggested reading and problem assign-
ment syllabi, and completely worked-out solu-
tions to all end-of-chapter problems and case
studies, including case studies from the first
(0-471-87324-1) 650 pages Available
February 1986
Carlos A. Smith, University of South Florida
Armando A. Corripio, Louisiana State
Unique in organization, treatment and content,
this incomparable text addresses the design
and analysis of industrial control systems by
presenting principles of physics, mathematics

and engineering and then applying them to
practical control problems.
(0-471-88346-8) 608 pages
Available 1985
Also of Interest:
Chi U. Ikoku, Pennsylvania State University
(0-471-89483-4) 517 pages 1984
Chi U. Ikoku, Pennsylvania State University
(0-471-89482-6) 503 pages 1984
Gael D. Ulrich, University of New Hampshire
(0-471-08276-7) 512 pages 1984
Mark E. Davis, Virginia Polytechnic Institute and State
(0-471-88761-7) 258 pages 1984
TRANSFER, Third Edition
James R. Welty, Charles E. Wicks and Robert E. Wilson,
all of Oregon State University
(0-471-87497-3) 803 pages 1984
Chi U. Ikoku, Pennsylvania State University
(0-471-81455-5) 277 pages 1985
For a complimentary copy of any of the above texts, contact your
Wiley representative or write to LeRoy Davis, John Wiley & Sons,
Inc., 605 Third Avenue, Dept. 6-6292, New York, New York 10158.
Please include course name, enrollment and title of present text.
605 Third Avenue
New York, NY 10158


Department of Chemical Engineering
University of Florida
Gainesville, Florida 32611

Editor: Ray Fahien (904) 392-0857

Consulting Editor: Mack Tyner

Managing Editor:
Carole C. Yocum (904) 392-0861

Publications Board and Regional
Advertising Representatives:

Gary Poehlein
Georgia Institute of Technology

Past Chairmen:
Klaus D. Timmerhaus
University of Colorado

Lee C. Eagleton
Pennsylvania State University

Richard Felder
North Carolina State University

Jack R. Hopper
Lamar University

James Fair
University of Texas

J. S. Dranoff
Northwestern University

Frederick H. Shair
California Institute of Technology

Angelo J. Perna
New Jersey Institute of Technology

Stuart W. Churchill
University of Pennsylvania

Raymond Baddour

Charles Sleicher
University of Washington

Leslie W. Shemilt
McMaster University

Thomas W. Weber
State University of New York

Chemical Engineering Education

3 The Ratings Race

The Educator
4 Ken Bell of Oklahoma State, Paul R. Couey

The Department
8 U.C. Davis, Pieter Stroeve

Award Lecture
12 Steady-State Multiplicity Features of Chemically Reacting
Systems, Dan Luss

Views and Opinions
18 Design, Accreditation, and Computing Technology,
Morton M. Denn
19 Expectations of the Competence of Chemical Engineering
Graduates in the Use of Computing Technology,
CACHE Corporation

22 A Note on Diffusive Mass Transport, Henry W. Haynes, Jr.
32 Teaching Technical Communication to Undergraduates:
A Matter of Chemical Engineering, Ralda M. Sullivan
36 A Physical Interpretation for the Gamma Distribution,
Kuttanchery A. Ramanarayanan, William K. Howard

28 Exploiting the On-Campus Boiler House, Donald R.
Woods, Philip E. Wood, Floyd H. Gallinger
40 Fluid Flow Experiment for Undergraduate Laboratory,
Viroj Vilimpochapornkul, Nsima T. Obot

44 Development of the Design Laboratory, Harry Silla

Class and Home Problems
48 Ripple in a Falling Film, Dale L. Schruben
2 Books Received
7 Letters to the Editor
2 Positions Available
21, 35, 43, 50 Book Reviews

CHEMICAL ENGINEERING EDUCATION is published quarterly by Chemical Engineering Division,
American Society for Engineering Education. The publication is edited at the Chemical Engineering Depart-
ment, University of Florida. Second-class postage is paid at Gainesville, Florida, and at DeLeon Sprngs
Florida. Correspondence regarding editorial matter, circulation and changes of address should be addressed
to the Editor at Gainesville, Florida 32611. Advertising rates and information are available from the adver-
tising representatives. Plates and other advertising material may be sent directly to the printer: E. 0.
Painter Printing Co., P. 0. Box 877, DeLeon Sprmings, Florida 32028. Subscription rate U.S., Canada, and
Mexico is $20 per year, $15 per year mailed to members of AIChE and of the ChE Division of ASEE. Bulk
subscription rates to ChE faculty on request. Write for prices on individual back copies. Copyright 1986
Chemical Engineering Division of American Society for Engineering Education. The statements and opinions
expressed in this periodical are those of the writers and not necessarily those of the ChE Division of the
ASEE which body assumes no responsibility for them. Defective copies replaced if notified within 120 days.
The International Organization for Standardization has assigned the code US ISSN 0009-2479 for the
identification of this periodical.


use CEE's reasonable rates to advertise.
Minimuim rate Vs page $60; each additional column inch $25.

INSTITUTE Assistant/Associate/Full Professor (ful year, full
time, tenure system). Biochemical engineering positions and
Distinguished Research Professorship. The Chemical Engineer-
ing Department and the Michigan Biotechnology Institute have
joint tenure system positions open. Rank, salary and incentives
commensurate with qualification. Applicants should have de-
monstrated ability in one or more of the following areas.
Bioreactor Design and Scale-up;p Product Separation and Re-
covery from Cell Culture Broths; Sensors, Controls and Com-
puter Interfacing of Biological Processes; and Renewable Re-
source Technology. Strong commitment to applied research plus
teaching limited to graduate training in biotechnology expected.
Applicants with outstanding credentials and an active research
program are encouraged to apply. The positions offer the excite-
ment of sharing in both the understanding and rewards of de-
veloping new technology. Qualified women and minorities are
encouraged to apply. Apply in writing to: Donald K. Anderson,
Chairperson, Biotechnology Search and Selection Committee,
Michigan State University, 173 Engineering Building, East
Lansing, MI 48824-1226. Applications are requested by Sep-
tember 1, 1985, but will be accepted as long as necessary to fill
the position.

Chemical Engineering-Assistant or Associate Professor-This
tenure-track position will involve approximately half-time
teaching and half-time research. We will help the successful
candidate establish research by providing initiation funds, co-in-
vestigation opportunities with senior faculty and proposal prep-
aration assistance from our Office of Engineering Research.
Candidates must possess an earned and accredited Ph.D. in
Chemical Engineering or related areas and have strongly related
qualifications. We welcome applications from candidates with
competencies and interest in any field of chemical engineering,
but especially seek those with strengths in controls and in-
strumentation. This position is available as early as July, 1986.
For full consideration applications should be received by March
30, 1986. Please send your resume and names of three references
to Professor Billy L. Crynes, Head, School of Chemical En-
gineering, 423 engineering North, Oklahoma State University,
Stillwater, OK 74078. Calls for additional information are in-
vited. OSU is an equal opportunity/affirmative action employer.

Applications are invited for tenure-track positions. Assistant
Professor level preferred, but outstanding candidates at senior
levels will be given full consideration. Distinguished record in
research, commitment to a dynamic research program, and abil-
ity to teach undergraduate and graduate courses is expected.
Experience in process simulation and design strategy,
biotechnology, or material science would be welcome. Send re-
sume, including names of three references, to Prof. H. Scott
Fogler, Chairman, Department of Chemical Engineering, The
University of Michigan, H. H. Dow Building, Ann Arbor, MI
48109. The University of Michigan is an equal opportunity, affir-
mative action employer.


Quarterly 4 See Attached Rates
CHEMICAL ENGINEERING EDUCATION, Room 317, Chemical Engineering Department,
University of Florida, Gainesville, Alachua, FL 32611
Chemical Engineering Divisioni American Society for Engineering Education,
11 DuPont Circle, Washington. DC 20030
PUBLISHER 1-t ami C- mplm Hjij~ U d.U- /
ASEE Chemical Engineering Division, 11 DuPont Circle, Washington, DC 20030

Ray W. Fahien, Chemical Engineering Department, Room 319,
University of Florida, Gainesville, FL 32611
Carole Yocum, Chemical Engineering Department, Room 317,
University of Florida, Gainesville, FL 32611

Official publication of Publisher as Any mail addressed o owner should go to
listeo above Editor as listed above.


2oe Ne8e M O GEiE coso ls unT a 0 L e a one ocno oc n.: on


fl o PRECEDING E cncuL 21941819
SA TOTALNo CCP, ES o 2398 1960

S certify that the statements made by RCULAT
me above are correct and complete e i Edtor

books received

Powder Technology, linoya, Beddow, Jimbo; McGraw-Hill and
Hemisphere Publishing Company, New York 10016; 823 pages

Advanced Organic Chemistry; Reactions, Mechanisms, and Struc-
ture, Third Edition, Jerry March; Wiley Interscience, Somerset,
NJ 08873; 1346 pages, $39.95 (1985)

Proceedings of the Sixth International Zeolite Conference, Edited
by David Olson and Attilio Bisio; Butterworth Publishers,
Stoneham, MA 02180; 1007 pages, $89.95 (1984)

Computer-Aided Design of Polymers and Composites, D. H. Kael-
ble; Marcel Dekker, Inc., New York 10016; 304 pages, $59.75 (1985)

Managing the Engineering and Construction of Small Projects, by
R. E. Westney; Marcel Dekker, New York 10016; 296 pages, $55
Special Functions for Engineers and Applied Mathematicians,
L. C. Andrews; MacMillan Publishing, New York 10022; 357 pages
Electron Correlation in Molecules, S. Wilson; Oxford University
Press, 200 Madison Ave., New York 10016; 281 pages, $59 (1984)
Press, 200 Madison Ave., New York 10016; 281 pages, $59 (1984)



Companies try to maximize their profits but uni-
versities and their departments try to maximize their
prestige. Unlike the profits of a company, the prestige
of a department is a non-quantitative entity: It repre-
sents the collective subjective opinion that the
academic community (and to a lesser extent, the pub-
lic) has of a department. It is reflected in the ratings
the department receives in the various surveys spon-
sored by educational organizations. The existence of
ratings catalyzes competition among departments for
more prestige and still higher ratings. Thus the tacit
goal of a department, as seen by many of its faculty,
is to compete with other departments for greater
prestige and higher ratings.
But unlike the competitive world of sports, the
social consequences of what is done in the university
are more important than how high it ends up in the
ratings. Whether Kansas City wins the World Series
or St. Louis does is of great importance to the follow-
ers of those teams, but since professional sports are
only games played for human entertainment, the out-
come has little import on society as a whole. However,
the work of academe, if it is to merit and receive public
support, must be more than just a game. And the
goals of the department must be based on something
more than a self-serving or group-serving competition
for high ratings.
What should be the goals of a department or of a
university? Different people have differing ideas: To
the research professors, the university is a place to do
research and to write papers and books; to the
teachers it is a place to disseminate knowledge and to
promote learning; to the students it is a place to get
good grades and a degree so that their employment
opportunities are enhanced; to the public it is a place
to send their children for an education, to get informa-
tion or advice from professors, or to enjoy entertain-
ment in the form of sports, plays, and concerts.
More generally, the goal of the university is not
profit making but service-service to society through
the seeking of knowledge (research), the dissemina-
tion of knowledge (teaching and publishing), and the
doing of other activities that are of value to society.
Thus, professors should be encouraged to do re-
search not because they seek prestige for themselves
or for the department or university, but because it is

known that knowledge-no matter how esoteric or re-
mote it may at first seem to be-has a tendency, even-
tually, to be useful to society.
But the work of the university is not only research:
A state university also has a responsibility to its stu-
dents, to the tax-payers, and to the profession to pro-
vide a good education as well as to do research. And,
one might argue, the private university has the same
responsibility to its students, its financial supporters,
and the profession.
Therefore, professors ought to be supported and
rewarded for using part of their time teaching or
working with individual students since by doing so
they are helping to prepare their students to serve
mankind-either in industry or as future teachers
The goal of a department, then, should be service
to society and not the pursuit of high ratings.
How does the goal of service differ from the goal
of seeking higher ratings? Let us take an example: If
the goal is service the department might develop a
program that is balanced with regard to teaching and
research, theory and experiment, basic research and
applied research, preparation for industrial employ-
ment or graduate work. But if the goal is to seek
higher ratings, it might follow a narrow specialized
path in which research is all that matters because it
thinks this has led to high ratings in the past (and will
do so in the future).
Ironically, many of the departments that have
achieved high ratings have not sought them as a main
goal. Nor have they necessarily de-emphasized teach-
ing and service. There are a number of excellent
teachers (Prausnitz, Bird) on the faculties of the lead-
ing universities as well as professors who served their
profession as directors and presidents of national
societies (Bill Corcoran) or served the community in
various ways (Neal Pings). Those who think that
academic excellence results from neglect of teaching
and service may some day find that the opposite is
true; that higher ratings do not come from a neglect
of teaching but from a concern for it and that the rat-
ers, consciously or unconsciously, do take teaching
into account when they mark their ballots.
Of course, good teaching is hard to define or mea-
sure, but somehow good teachers become known and
talked about and appreciated by former students and
colleagues. It is an ironic twist that a self-serving goal
zealously sought after (e.g., happiness, prestige) often
is elusive but is attained when a higher goal of service
is substituted.
Ray W. Fahien


P1 "educator

ken Bell

of Oklahoma State

Oklahoma State University
Stillwater, OK 74078

To describe Kenneth J. Bell, 55, Regents Profes-
sor of Chemical Engineering at Oklahoma State Uni-
versity, and internationally recognized authority on
heat transfer, can be as complex as trying to solve
some of the complex problems this highly specialized
field can present. He is, first, a highly competent en-
gineer blessed with the ability to handle both the
theoretical and applied aspects of his field. He is also
a husband, father, oneologist (wine expert), collector
of fine books, mineralogist, avid reader, and keen
amateur historian. As one graduate student puts it: "I
understand Dr. Bell's father was an engineer. He
wanted to be a historian. Thank God his father had
some influence over him." He is also the unofficial,
red-pen editor for the School of Chemical Engineer-
ing. As School Head, Dr. Billy Crynes says, "He is
our unofficial grammarian. He takes great pains (and
delight) in editing colleague's and student's papers.
It's impossible to slip anything by him."
Ken Bell was born in Cleveland, Ohio in 1930. He
received his BS degree in chemical engineering from
the Case Institute of Technology in 1951, his MChE
from the University of Delaware in 1953, and his PhD
in chemical engineering from the University of Dela-
ware in 1955. A year after receiving his doctorate
from Delaware, he met and married Karen McLe-
more, a tall, striking woman who seems to compliment
Ken's dynamo vitality with a controlled, inward calm-
ness. Ken and Karen have four children: Lorna, 27,
also a chemical engineer; Craig, 24, with the U.S.
Army; Tamra, 24, a youth worker; and Ellen, a 14-
year-old ninth grader who, according to her mom, is
a budding ballerina. Karen relates that she and Ken

Ken's real expertise lies in the
analysis and evaluation of data to provide the best
design of heat transfer equipment. His pragmatic
philosophy is echoed by a student who says,
"The homework .. is very applied."

met while he was working as an engineer with the
heat transfer unit, Pile Engineering Department, at
the Hanford Atomic Products Operation in Richland,
Washington. The area, she says, afforded Ken the op-
portunity to climb many of the Pacific Northwest's
numerous mountains. However, she says, "Since mov-
ing to the Southern Plains of Oklahoma, he has had to
make do with climbing the four flights of stairs in the
engineering building."
Karen describes her husband, too, in glowing
terms like: "He enjoys good food and will eat almost
anything .... except peanut butter. . and, to most
folks consternation, he does not put weight on easily."
Karen also comments on Ken's editing prowess. "Ken
has the curse of being a natural speller (unlike his
wife). Mispelled words simply pop out at him from
everywhere. He's been known to whip out his red pen-
cil to make corrections on whatever is at hand."
Following his Hanford experience, Ken was assis-
tant professor of chemical engineering at Case Insti-
tute of Technology for six years. After serving as vis-
iting faculty member for the Oak Ridge School of

Copyright ChE Division, ASEE, 1986


Reactor Technology in 1958, and spending a summer
as research professor at the University of Delaware
in 1959, he came to Oklahoma State University in 1961
as associate professor of chemical engineering. OSU
chemical engineering school head, Billy Crynes, says
he first met Ken in 1967 when he came to work for
the university. "My first impression," he says, "was
that this is one arrogant s.o.b. He says things in 25
words that should take 5."
But, Ken Bell is good. He's one of a handful of
recognized experts in the world in heat transfer. His
publishing and consulting records speak for them-
selves. He has published four major books, 46 techni-
cal papers and formal reports, 16 monographs, sur-
veys, and handbook sections, 7 articles and 6 book
reviews. He has consulted with more than a score of
firms, both in the United State and abroad. Industry
giants such as U. S. Steel, Phillips Petroleum,
Rockwell International, the Argonne National Labo-
ratory and Mitsubishi Heavy Industries of Japan are
among those who seek Ken's advice. Yet, while his
consulting work has been broad, Billy Crynes says
that, ". . .in fact, he does relatively little consulting
when one considers his expertise. Even more, despite
all the time pressures, he is the first one to help out
when committee assignments are made. And, when
he takes on a job, he is very thorough. He was asked
to serve as head of the University Academic Appeals
Board, a very tough job. He spent hours on that Board
reviewing cases, and when it was all over, he received
glowing praise for the work he had done."
Ken Bell's influence also reaches a broad spectrum
of national and international groups and organizations.
He was a committee member of the National Research
Council-Army Research Office Advisory of the Na-
tional Academy of Sciences. From 1971-75, he was the
U. S. Delegate to the Assembly for International Heat
Transfer Conference in Tokyo. And, he is a member
of the Scientific Council of the International Center
for Heat and Mass Transfer in Belgrade, Yugoslavia,
the International Council of Revue Generale de Ther-
mique in Paris, and the National Science Foundation's
Cooperative Research Program in Heat and Mass
Transfer between the United States and the Soviet
Union. In addition to his consulting work, teaching
and research duties, Ken serves in important editorial
positions. In 1977, he was named editor-in-chief of
Heat Transfer Engineering, an international quar-
terly. He is a member of the editorial board of the
Heat Exchanger Design Handbook and served as
editor of Advances in Cryogenic Heat Transfer, a
chemical engineering symposium series. His short
courses and lecture series have been taken all over
the world. He has developed OSU engineering exten-

sion courses which have been held throughout the
United States. Finally, he has been asked to deliver
over 30 major talks to engineering groups and other
colleges and universities throughout the United
States and the world.
Naturally, Ken Bell's accomplishments have not
gone unnoticed. In 1978, he was awarded the Donald
Q. Kern Award by the American Institute of Chemical
Engineers. Ken was a friend and professional col-
league of the late Dr. Kern, an educator, author and
pioneer in the art and science of process heat transfer.
In 1980, the Oklahoma Society of Professional En-
gineers named Ken as Outstanding Engineer. In 1972,
he was awarded the Best Paper Award at the 12th
Annual Heat Transfer Conference held in Tulsa. The

Ken is the recipient of numerous awards.

paper, "Friction Factors for Inline Square Tube
Banks at Low Reynolds Number," was co-authored
by K. Ishihara. Ken is listed in Who's Who in
America, Who's Who in the South and Southwest,
American Men and Women of Science, Who's Who in
Engineering, and Who's Who in Technology Today.
Despite his international reputation in heat trans-
fer, it is in the classroom and with students, both
graduate and undergraduate, that he excells.
Longtime friend, colleague, and former technical di-
rector of the Heat Transfer Institute in California,
Jerry Taborek, says that, "Ken has an outstanding
ability to explain even complicated problems in a com-
prehensive way-and if one is lucky enough to get the
rare chance to say something-Ken would listen pa-
tiently, but you better be well prepared."
Graduate students are even more expressive when


asked to relate their experiences with Dr. Bell. "His
classroom presentation is friendly, but professional,"
according to one student. "He has," says another
graduate student, "a solid command of what he
teaches in any subject he teaches. The thing about
him I like is that if he doesn't know the answer to a
question right away, he'll tell you he doesn't know,
and will find the answer for you." "His international
reputation," offers another student, "makes him cre-
ditable in the classroom. Also, if you take Dr. Bell's
courses, or are one of his graduate students, you'd
better be prepared to work and work hard. If you
don't, you will fail. If you do, you will benefit greatly
and Dr. Bell will be there to help you the whole way."
But, one student cautions that this guru-student re-
lationship may sometimes be fraught with danger: "If
you ask Dr. Bell a question, you're not likely to get a
direct reply then. More than likely, he'll ask you what
you think about the problem. And, you better have
thought about it, or be adequately prepared to think
on the spot about a solution. He just doesn't like to
give out unearned answers."
All of Ken Bell's students indicate that he is very
tough in the classroom, and somewhat intimidating to
young undergraduate students. He is also an under-
standing pedagogue. "Dr. Bell," says one, "is always
compassionate with students. Although he is busy, he
seems genuinely concerned about all his students and
personally knows all of his junior, senior and graduate
Humor is not an absent element in a Ken Bell class-
room, either. "His classes are not strict and formal.
They are full of anecdotes that help lighten the mood.
You certainly don't fall asleep. They're not boring,
and you learn," says one student. And, although Ken's
taste for wine is legendary (Dr. Crynes tells about an
incident in a restaurant about wine refusal, initiated
by Ken, and upheld by the maitre d'), the students
relate how they look forward to . .Dr. Bell's lec-
ture on the distillation of fine Scotch whiskey."
Despite his professional credibility, however, Ken
Bell remains the consumant teacher. "He's always
curious about what you are doing," says one student.
"He'll talk with you for hours if you're prepared," says
another. "Ken Bell," says Dr. Crynes, "is a spellbind-
ing speaker. He is knowledgeable and anecdotal. I dis-
covered this the first time he gave a guest lecture in
one of my classes. He conveys such a feeling of confi-
dence that it really can be overwhelming."
Ken's real expertise lies in the analysis and evalu-
ation of data to provide the best design of heat trans-
fer equipment. His pragmatic philosophy is echoed by
a student who says, "The homework you do is very
applied. All his students have a sense that they will

A rare moment of relaxation for Ken and Karen.

definitely be able to use the material in the real world
when they graduate." This down-to-earth, no-fancy-
stuff attitude was, perhaps, best reflected by Ken
himself in an article in Heat Transfer Engineering
dealing with the problems of remaining "computer lit-
erate" in today's world:
.... don't lay any guilt trips on me about
computer literacy-I'm about as literate as
my time allows and my job requires now,
and I'll become as literate as I need to be
for tomorrow's job.
If Ken Bell has any shortcomings, it is his apparent
aversion for physical activity. Dr. Crynes says, "He
loathes routine physical exercise. "In fact," Dr.
Crynes, himself an avid and consistent jogger, says,
"Ken celebrates his dislike for exercise by ritually
taking a brisk, around-the-block walk with the family
dog once a year. Of course, his good shape and lean
appearance are a constant source of amazement and
envy among his close friends and colleagues. (Karen
admits that Ken tries to walk the dog around the block
when he can.)
Perhaps Crynes' assessment of Ken Bell's value to
the OSU faculty and the rest of the engineering pro-
fession best sums up his influence and place in the
world: "Ken is something special and unique. He is
one of the few persons I have had the opportunity to
know who excells in both the theoretical and applied
aspects of his field. He has fulfilled all the university
obligations expected in teaching, service, research,
and national and international reputation. But,
perhaps Ken's greatest value is the rippling effect he
has on other faculty members. His tremendous talent
and energy inspires others to reach the higher levels
of knowledge and achievement in their own fields. This
halo effect definitely touches everyone who comes in
contact with Dr. Kenneth Bell." El


IIM letters


Dear Editor:
Professor Barduhn's letter in the last issue of CEE noted that
the prefix "a" to a word often infers the negative (e.g., symmetric
vs. asymmetric), and that this should apply to diabeticc" and
"adiabatic." Consequently, non-adiabatic should have the same
meaning as diabetic. This is an interesting thought.
I wonder whether Professor Barduhn is aware that the word
bat is the root of all these words. Performing the usual series expan-
sion on that little word:
1. We first obtain batic which means to act like a bat, or to be
2. Then comes abatic which refers to non-batlike behavior.
3. Obviously diabetic, must mean to behave like two non bats,
or to not be batty twice in a row (there is still some argument
about these different interpretations).
4. Continuing this series expansion by adding another prefix "a"
then gives adiabatic, which, without question, refers to not
behaving like two non-bats.
5. And finally, we are impelled inexorably by this crescendo of
steely logic to conclude that non-adiabatic means to never not
behave like two non-bats, at least not two times in a row,
nohow, nowhere and at no time-not never.
But what has this to do with hot air and heat flow?
Octave Levenspiel
Oregon State University


Dear Editor:

Those involved with chemical engineering education might be
interested in our videotape series.
The Women In Science Videotape Series consists of eight vid-
eotapes designed to present women scientists and students from
across the country in an upbeat and positive light. Seven of the
tapes focus on women in the following fields: biomedical science,
chemistry, computer science, dentistry, engineering, geoscience,
and physics/astronomy. The eighth videotape features general
career opportunities in science and addresses the barriers that dis-
courage young women from pursuing science careers.
Funded by a grant from the Women's Educational Equity Act
Program of the U. S. Department of Education, the videotapes are
intended to encourage young women to take high school and college
courses in math and science and to seriously consider careers in
science or technology. The series was designed to be used by sec-
ondary school and college instructors or counselors, and is appropri-
ate for career fairs, classroom use, individual counseling sessions,
and public television.
Each color videotape cassette is approximately thirty minutes
long and is available in two formats: 3/4-inch U-matic or 1/2-inch
VHS. Included with the videotapes are brochures/posters contain-
ing specific career information for each of the fields. A user's guide
accompanies each of the first seven videotapes and contains pre-
and post-viewing activities, discussion questions, salary informa-

tion, additional resources, and the videotape script. These tapes
are currently available for preview rentals or purchase.

Joyce B. Williams
Women in Science
Educational Resources
University of Michigan
Ann Arbor, MI 48109


Dear Editor:
Those who teach chemical engineering thermodynamics know
how difficult it is to find suitable examples which are realistic and,
at the same time, give good insight into the scientific significance
of thermodynamics. Those who teach plant design are concerned
with finding problems that reflect industrial reality but at the same
time do not excessively burden the student who has only limited
time for performing complex calculations.
With ever-increasing use of computers in chemical process de-
sign, teachers of chemical engineering are properly concerned about
giving students some experience in the use of computers for solving
industrially-significant problems. In response to this concern, we
have established some case-study problems in applied chemical
thermodynamics which may be of help to chemical engineering
teachers, especially in plant-design courses.
Each of the case-study problems, briefly described below, pres-
ents first, some introductory background information; second, a
statement of the design problem; and third, the necessary ther-
modynamic framework for formulation of the problem toward a sol-
ution. To assist in reaching a solution, each case study also includes
some self-explanatory examples in addition to the necessary com-
puter programs and subroutines. For each program, we give input
and output information as well as program documentation that ex-
plains how to use the programs and describes the subroutines.

1. Vapor-Liquid Equilibria for the System Acetone-Methanol. Ef-
fect of Pressure on Azeotropic Composition is concerned with
vapor-liquid equilibria for an azeotropic mixture obtained from pro-
duction of methanol by oxidation of butane [1]. At preo-res close
to atmospheric, the acetone/methanol mixture has an azeotrope
which contains 83 mol percent acetone. The problem is to find the
pressure range where no azeotrope exists, allowing complete sep-
aration by distillation. To describe the thermodynamic behavior of
the vapor, we use the virial equation of state, truncated after the
second virial coefficient, with virial coefficients obtained from the
Hayden-O'Connell correlation [2]. Activity coefficients for the liquid
phase are determined from the UNIQUAC equation. The two-di-
mensional Newton-Raphson iteration technique is used to solve the
equations that give the conditions where no azeotrope is formed.

2. Vapor-Liquid Equilibria for Aqueous Mixtures of Weak, Vol-
atile Electrolytes and Other Gases, is concerned with aqueous mix-
tures of weak, volatile electrolytes as found, for example, in coal-
gasification processes, where aqueous streams containing NH3,
C02, H2S, or SO2 must be purified. To design equipment for purifi-
cation by stripping, it is necessary to calculate vapor-liquid equilib-
ria for aqueous mixtures containing these volatile solutes that par-
tially ionize in water. To describe the behavior of volatile, ionizing
solutes in water, we must satisfy simultaneously phase equilibria
and chemical (ionization) equilibria, along with the constraints of
material balances. The program provides necessary computer de-
tails to achieve the desired simultaneous solution; in addition, the
program enables the user to do dew-point, bubble-point and flash
Continued on page 51.


Bainer Hall is the home of the Department of Chemical Engineering.

j npo Mdepartment


University of California at Davis
Davis, CA 95616

IN 1906, THE UNIVERSITY of California acquired
768 acres surrounding the town of Davisville for a
University Farm. The Farm (as U.C. Davis was orig-
inally known) offered instruction in principles and
practices of managing soils, crops, and animals. After
the establishment of the Colleges of Agriculture, Let-
ters and Science, and the School of Veterinary
Medicine, U.C. Davis was declared a general campus
of the University of California in 1959. The College of
Engineering was founded in 1962. The School of Law
held its first classes in 1966, and the School of
Medicine admitted its first students in 1968.
With a present student enrollment of about 20,000,
U.C. Davis h1as matured into a full university commu-

Copyright ChE Division ASEE 1986

nity while retaining its original character as a close-
knit and friendly place to learn and to conduct re-
search. The campus is located on a 3,800 acre site in
the Sacramento Valley which has been growing
economically ever since the gold rush days. The
Pacific Ocean, San Francisco Bay, Napa Valley and
the spectacular Mendocino Coast lie to the west of
Davis. To the east, the Sierra Nevada mountains pro-
vide skiing in the winter and hiking in the summer.
Lake Tahoe provides many scenic views and year-
round resort activities. Whale watching in California's
delta (South of Davis) has recently become a favored
The city of Davis has received national recognition
for its energy conservation policies. Davis' energy-
saving building code, retrofit ordinance, recycling sys-
tem, bike lanes, and extensive use of solar energy
make it one of the most progressive cities in America.


In 1959, Clark Kerr, President of the University
of California, set up a state-wide committee to look
into the future of engineering education in the univer-
sity. There were representatives from all the cam-
puses, and Roy Bainer represented Davis. Kenneth
Pitzer, Dean of Chemistry and Chemical Engineering
at Berkeley, was chair of the committee, and the
meetings were held at Berkeley. Because U.C. Davis
had a program in engineering since 1915, had a
cooperative degree with engineering at U.C. Ber-
keley, and had many engineers in other departments,
Dean Pitzer believed that a logical place to start a
new engineering college was at U.C. Davis. In 1961
Roy Bainer set up a local committee to propose and
implement an engineering program at Davis. One of
the members of that committee was Joe Mauk Smith
who had come to the Department of Food Science and
Technology in July 1961. Joe Smith was head of a sub-
committee appointed to study the development of
chemical engineering within the proposed college of
The Davis program was adopted by the state-wide
committee and the president. In 1962, the Regents
authorized the College of Engineering and appointed
Roy Bainer as its first dean. In the fall of 1962, the
Regents extended the college at Davis to include the
Lawrence Radiation Laboratory at Livermore, and in
1963 a Department of Applied Science with facilities
at both U.C. Davis and Livermore was established.
The College of Engineering now has six engineer-
ing departments, (Agricultural Engineering, Applied
Science, Chemical Engineering, Civil Engineering,
Electrical and Computer Engineering, and Mechanical
Engineering) two divisions (Computer Science and
Materials Science) three interdisciplinary graduate
groups (Biomedical Engineering, Computing Science,
and Engineering Management) and offers a broad
range of engineering programs. Under Dean M. S.
Ghausi's leadership, undergraduate and graduate en-
rollments have gone up to approximately 2,000. The
college is among the top 20 grantors of Ph.D. degrees
awarded in the United States (according to the En-
gineering Manpower Commission) and awards more
than 300 Bachelor of Science, 100 Masters and 35 Doc-
toral degrees annually.

In 1962, the new College of Engineering consisted
of one department and several programs, one each in
separate areas of engineering. Joe Smith as head of
the chemical engineering program, recognized that if
chemical engineering were to develop as a recognized

discipline at U.C. Davis, a separate department was
necessary. A few faculty members in the college felt
strongly that there should not be separate depart-
ments of engineering. However, Joe Smith's views
prevailed and, after the Department of Applied Sci-
ence had been established, the faculty approved the
establishment of a Department of Chemical Engineer-
ing to be effective July 1, 1964. The only faculty mem-
bers in the new department were Joe Smith (Chair),
Bruce Caswell, Stephen Whitaker and Richard Bell.
After the establishment of the department, the de-
velopment of a strong program in chemical engineer-
ing was initiated. This development did not occur

In 1962, the new College of Engineering
consisted of one department and several programs,
one each in separate areas of engineering. Joe Smith
. recognized that if chemical engineering were to
develop as a recognized discipline . a
separate department was necessary.

without a struggle, since there was still strong sup-
port in the college for a common curriculum for all
engineering students and the department had to jus-
tify the establishment of courses such as ther-
modynamics and fluid mechanics separate from the
existing courses in these subjects taken by all other
students in the college. In time the support for a com-
mon curriculum dwindled and the department's pro-
grams were well-established in the late sixties.
The faculty has grown steadily since those earlier
days: Ben McCoy and Alan Jackman, both alumni of
Minnesota arrived in 1967 and 1970; Ruben Carbonell
and David Ollis joined the department, in 1973 and
1980 respectively, but are now at North Carolina
State University; Pieter Stroeve and Dewey Ryu,
both with backgrounds at the Massachusetts Institute
of Technology, joined in 1982; Brian Higgins, another
Minnesota alumnus, and Roger Boulton, from the Uni-
versity of Melbourne, arrived in 1983; Ahmet
Palazoglu, from Rensselaer Polytechnic Institute, and
Karen McDonald, from the University of Maryland,
are the most recent additions to the faculty. Ben
McCoy is the third and present Chair, succeeding
Richard Bell who, in turn succeeded Joe Smith.
Former faculty members (Bruce Caswell, Neil
Dougharty and Frank McLarnon) have contributed to
the development of the department.

The Chemical Engineering Department at U.C.
Davis has been distinguished by a continual succession
of outstanding students and a devotion by the faculty
to excellent teaching. In the past eight years, three
members of the department-Alan Jackman, Stephen


Whitaker and Pieter Stroeve-have received the col-
lege's Teaching Award. Several outstanding teaching
texts have been authored or co-authored by the facul-
ty. Joe Smith and Hank van Ness of R.P.I. are the
co-authors of Introduction to Chemical Engineering
and Joe Smith is sole author of Chemical Engineering
Kinetics. Stephen Whitaker has written an Introduc-
tion to Fluid Mechanics, Elementary Heat Transfer

Minicomputers are extensively used in teaching and re-
search. Ahmet Palazoglu and a graduate student discuss
results of a program.

Analysis and Fundamental Principles of Heat Trans-
fer. These texts have made their impact not only on a
generation of Davis students but also on students in
other institutions across the country and around the
The undergraduate course curriculum at U.C.
Davis is very rigorous. The number of quarter units
required for graduation is 193. Our graduates have
benefitted from the program and they have been very
successful in both industry and academic institutions.
The majority of the students are employed in the oil
and chemical industry, but in the past few years
nearly one-third of our students have obtained jobs in
the thin film technology (integrated circuits, magnetic
media, etc.) and biochemical engineering industries.
Despite their heavy course load, our students are
involved in university cultural and extra-curricular ac-
tivities. The student chapter of the American Insti-
tute of Chemical Engineers is particularly active and
organizes athletic, educational and social events. Fac-
ulty also participate in events like hiking once each
year to the peak of Mount Lassen in the middle of the
The department offers graduate programs leading
to the MS and PhD degrees. They provide the ad-
vanced student with a strong background in modern
chemical engineering theory and its relationship to

chemical engineering processing, through formal
course work and individual research. The PhD candi-
date is required to pass a preliminary examination,
given by the department after two quarters of resi-
dence, and a qualifying examination administered by
the graduate division. The latter examination covers
the candidate's area of research and two minors of the
candidates choice. Before submitting and defending
the PhD thesis, the student takes at least 60 quarter
units of coursework including two minors, each of 15
units minimum. In both the MS and PhD program,
the student normally takes 19 units of core courses in
chemical engineering.

Traditionally, the department has been strong in
the areas of reaction engineering, separations and
transport phenomena. With the addition of new fac-
ulty in recent years, other areas of research have been
strengthened or initiated-in particular, process
dynamics and control, rheology, coatings, biotechnol-
ogy, and thin film technology. The department has
close ties with the Department of Viticulture and
Enology (the world's premier department of wine sci-
ence). Dewey Ryu and Roger Boulton have joint ap-
pointments in the Department of Chemical Engineer-
ing and the Department of Viticulture and Enology.
Interdisciplinary research is a strong tradition on the
Davis campus and research interactions exist with the
Department of Electrical and Computer Engineering,
the Mathematics Department and the School of
Medicine. However, chemical engineering research
receives the greatest attention. A description of the
research programs follows.

Multiphase Transport Phenomena
The analysis of the transport of heat, mass and momentum in
multiphase systems is of major concern to Stephen Whitaker. His
analysis is based on the local, volume-averaged form of the point
equations, i.e., the Navier-Stokes equations, the diffusion equation
and the thermal energy equation. The method of volume averaging
provides the form of the local, volume-averaged transport equations
and the effective transport coefficients. The latter are determined
by means of a closure scheme, and much of Whitaker's current
work on the fundamental aspects of multiphase transport
phenomena is directed towards the closure problem. In addition to
his fundamental studies, Whitaker is working on a variety of prac-
tical applications such as drying porous media, design of packed bed
catalytic reactors, and single and two-phase flow in porous media.
In collaboration with Pieter Stroeve, he is conducting a research
program on diffusion with chemical reaction in multiphase media
which has important applications in drying phenomena, transport
in cellular suspensions, and mass diffusion and heat transport in
porous catalysts.

Reaction Engineering
Accounting for transport rates and chemical kinetics gives the
basis for design of chemical reactors. Joe Smith and his research


group have been involved in determining the significance of, and
interaction between, these physical and chemical processes for vari-
ous types of catalytic reactors. His research has led to experimental
studies of rate parameters by dynamic and steady-state methods in
slurry, trickle-bed, single-pellet, and fixed-bed laboratory reactors.
Several of the most recent problems in this area involve develop-
ment of models for production of alternate fuels, such as supercrit-
ical extraction of hydrocarbons from shale, lignite, coal, and thermal
processes for producing liquid fuels from heavy oils and shale. Such
applications are particularly challenging since they include numer-
ous transport and chemical reaction steps in a multiphase environ-
ment. In collaboration with Ben McCoy, Smith has devised a novel
experimental approach to study the fundamental kinetics of
homogeneous and heterogeneous catalytic reactions. The method
has application to the study of S02 oxidation, a reaction in the
environment leading to acid precipitation. The method has also been
applied to the study of hydrogenation reactions.
Ben McCoy and Joe Smith are also probing the interaction be-
tween adsorption at solid surfaces and subsequent chemical reac-
tions. Dynamic experiments yield information which is not possible
to obtain with a steady-state system. This work is important in the
analysis and design of trickle-bed and slurry reactors.

Environmental Engineering

The kinetics of ion exchange and heavy metal adsorption on soils
is of concern to Alan Jackman. Ion exchange reactions are known
to be extremely rapid, with the overall rate being controlled by
mass transport. Recent studies have shown that Fickian, effective
diffusivity models are not able to predict the rates of ion exchange
by large, low-porosity particles composed of clay minerals. Experi-
mental and theoretical studies are conducted both to develop new
models and to understand better the limits of existing models. In
addition, work is in progress to identify the bonding mechanism of
heavy metal ions adsorbed by natural sediments. This work has
important implications for hazardous waste management.
Liquid hydrocarbon sources exposed to the atmosphere acciden-
tally or in chemical processes are a significant source of air pollu-
tion. The hydrocarbon sources are of many kinds, including wastes
in the soil, emissions from tanks and spills involving a variety of
liquids. The characterization of the mass transfer rates of volatile
components from pools of crude oils is being investigated by
Richard Bell. Measurements of the diffusivities of various
molecules in the crude oil are being conducted and the results are
used in models of the transport process. These models include the
energy budget, turbulent transport in the atmosphere, and the
transport processes in the liquid and gas interface.


Richard Bell is studying mass transfer phenomena on distilla-
tion trays. The department has a large-scale, air-water distillation
column simulator. A fiber optic technique has been developed for
obtaining residence-time distributions at a point on an active distil-
lation tray. Highly non-ideal residence time distributions have been
observed and were related to tray efficiencies. Present studies in-
clude the measurement of the two components of dispersion in the
plane of the tray. These results will be used in developing tray
design and scale-up criteria.
Ben McCoy is studying the use of affinity and hydrophobic
chromatography for large-scale, energy-efficient, high-resolution
separations. Mathematical methods, including the moment
techniques, are being applied to describe transport and kinetic pro-
cesses occurring in these column operations.
The fundamentals of membrane separation processes are studied
by Pieter Stroeve and his research group. The use of facilitated

A graduate student in Dewey Ryu's laboratory prepares
data acquisition and analytical apparatus for a fermen-
tation experiment.

transport in increasing the mass transfer rate of a desired species
across a membrane barrier is explored both theoretically and ex-
perimentally. The group is studying the use of porous membranes
to control transport rates of species.

Biotechnology, specifically biochemical engineering and biomed-
ical engineering, has always been an active area of research in the
department. A number of faculty are currently active in this field.
Roger Boulton's research involves chemical engineering aspects of
fermentation kinetics, process simulation, adsorption phenomena,
and process control and simulation of enological operations. He is
an leading authority on wine equipment selection, winery design
and layout, and the economics of investment and operation.
Dewey Ryu's research endeavors are primarily focused on the
application of biochemical engineering principles to the production
and effective utilization of renewable resources for feedstock,
energy and food utilization. Examples of his current research work
include application of immobilized enzyme and whole cell systems,
production and characterization of proteins and lipids of microbial
source, genetic improvement of yeast strains by gene manipulation
and protoplast fusion, continuous animal and plant cell culture
techniques, and problems associated with the instability of recom-
binant plasmids.
Karen McDonald, who joined the department this fall, is in-
terested in the control and optimization of biochemical processes.
Fermentation processes are inherently nonlinear, multivariable
processes in which many important process variables cannot be
measured on-line in real time. Further, fermentation systems are
time-varying as microorganisms change or adapt to their environ-
ment. Recursive estimation algorithms, based on optimal estima-
tion theory, are used in conjunction with dynamic process models
to estimate state variables between off-line sampling times. In col-
laboration with Ahmet Palazoglu, McDonald also investigates the
control and optimization of bioseparation processes. Several other
faculty members, including Pieter Stroeve, Richard Bell and Ben
McCoy, are interested in fermentation or the bioseparation of fer-
mentation products.
In the area of biomedical engineering, Richard Bell is inves-
tigating the effects of hyperbaric exposure on the human body.
Present work is directed toward the use of platelet loss at liquid-gas
interfaces in the blood as a measure of hyperbaric stress. Experi-
Continued on page 39.


Awa4d 2ecwe



The ASEE Chemical --
Engineering Division Lec- -
turer for 1985 is Dan Luss
of the University of Hous- ~ -
ton. The 3M Company pro- -I
vides financial support for
this annual lectureship
A native of Tel-Aviv, _
Israel, Dan Luss began .
his chemical engineering
studies at the Technion, Is- ''
rael, receiving his BSc de- \- '
gree in 1960. He then -: -
served in the Israeli Army and worked for a year as
an engineer in the military industry, where he became
aware of rapid chemical reactions and runaway of
explosive materials.
He returned to the Technion in 1962 and obtained
an MSc degree in 1963, conducting an experimental
study of direct contact heat transfer. He then attended
the University of Minnesota conducting research
under the direction of N. R. Amundson. After receiv-
ing his degree in 1966 he served as a visiting assistant
professor at Minnesota and joined the ChE depart-
ment at the University of Houston in 1967, where he
became the chairman in 1975.
Professor Luss has been the recipient of both the
Allan P. Colburn and the Professional Progress
Awards of the AIChE in 1972 and 1979, respectively.
He received the Curtis W. McGraw Award of the
ASEE in 1977 and was elected to the National
Academy of Engineering in 1984. He received the Dis-
tinguished Faculty Award from the University of
Houston in 1984.
Professor Luss has conducted extensive theoretical
and experimental research in the area of chemical
reaction engineering. He has worked on topics such
as steady state multiplicity and dynamics of chemi-
cally reacting systems, kinetics of grouped species,
performance of trickle bed reactors under pulsed flow
conditions, and flickering of catalytic gauzes. He has
introduced several new mathematical tools to the
analysis of engineering problems.

University of Houston
Houston, TX 77004

exhibit different steady states under the same
operating conditions. For example, a powder may flow
at two different rates in a standpipe under the same
pressure gradient [1], a diode may produce different
current levels under the same voltage drop, a laser
may transmit light at two different intensities for the
same impinging field, and a chemical reactor may yield
different amounts of the desired product at the same
operating conditions. A common feature of all these
systems is the occurrence of nonlinear flux-force rela-
tions and some feedback (communication) mechanism.
New mathematical tools for studying the qualita-
tive features of nonlinear systems have significantly
advanced our ability to understand and predict the
behavioral features of these systems. I believe that
these techniques will lead to many practical applica-
tions and become an important part of the mathemat-
ical training of ChE students. I shall restrict this pre-
sentation to problems encountered in chemically
reacting systems, even though many other applica-
tions exist.

The first analysis of steady-state multiplicity in a
chemical reactor was presented by Liljenroth in 1918
[2]. Ten years later, Semenov [3] developed the foun-
dation of the thermal explosion theory. Davies [4] dis-
covered experimentally two stable steady states dur-
ing the oxidation of hydrogen on a Pt wire in 1934.
The thermokinetic theory of heterogeneous reactions
was developed by Frank Kamenetskii in 1938-39 [5],
and Zeldovich and Zysin [6] analyzed the bifurcation
diagrams of conversion versus residence time in a
homogenous CSTR and discovered the existence of
isolated branches.
Surprisingly, these results had been overlooked by
most investigators in the West, and the main interest
in this subject was motivated by the pioneering works
0 Copyright Che Division, ASEE, 1986


... a powder may flow at two different rates in a standpipe under the same pressure gradient,
a diode may produce different current levels under the same voltage drop, a laser may transmit light at
two different intensities for the same impinging field, and a chemical reactor may yield
different amounts of the desired product at the same operating conditions.

of Van Heerden in 1953 [7] and by Bilous and 20
Amundson in 1955 [8]. A very large number of MULTIPLICITY
theoretical and experimental studies of steady state 18 FOR SOME Da
multiplicity were conducted in the following two dec- 1
ades and led to a rather comprehensive understanding 16
of the behavior of systems in which a single chemical 14 -
reaction occurs.
The most comprehensive resuhLs were obtained for 12 20 05
a continuously stirred-tank reactor (CSTR) in which a c- n = 3.0 1.0 0
single chemical reaction occurs. The species and a 0
energy balances can be combined in this case to give E 8
a single steady state equation of the form
x = Da f(x) (1)

where x is the conversion, Da is the ratio between the
characteristic time for flow (V/q) and for the chemical
reaction [CAr(CAf)], and f is a dimensionless rate ex-
pression which satisfies the condition that df/dx is
negative for x 1.
For example, when an nth order, irreversible
exothermic reaction is carried out in a cooled CSTR

f = (1 x)n exp x (2)


T = qpcp T + UaTc
r qpc + Ua

y RTr

0' I- II I I I I- I I
0 1 2 3 4 5 6 7 8 9

FIGURE 1. The dependence of the minimal value of the
activation energy for which steady state multiplicity
exists for some Da on P and the reaction order.

Explicit analytical expressions for y-m are available
for first and zeroth order reactions, namely

ym(8,1) = 4(1 + 1/6)

pc = Tf + UaTc/q

y characterizes the sensitivity of the reaction rate con-
stant to temperature changes and p is the dimension-
less temperature rise at complete conversion.
It can be shown that steady state multiplicity can
occur if and only if [9]
d in f(x) > (4)
d in x

for some x, i.e. the rate expression must be a non-
monotonic function of the conversion. Condition (4)
can be used to prove that for an exothermic, irrever-
sible nt-order reaction multiplicity can occur for some
Da if and only if [10-12]

y > ym(B,n) (5)

(1+B0)2/1 8<11
Ym(,0O) = 8J
4 e>,1

For all other reaction orders ym can be found by solv-
ing a simple cubic equation [10-12]. Figure 1 shows
this relation, indicating that for a fixed p, -Ym increases
with increasing reaction order. Similar results have
been obtained for other rate expressions and reactor
Most practical control and start-up problems as-
sociated with steady-state multiplicity are encoun-
tered in systems in which several reactions occur
simultaneously and are caused by the "taking over" of
an undesired reaction, the rate of which is negligible
at the standard steady state. This event is usually
accompanied by a high rate of heat release which may
lead to a runaway, or even to an explosion. Unfortu-
nately, the behavior of these systems is often very


intricate and the coupling between the various reac-
tions introduces new qualitative features which cannot
be predicted from available information about the
single reaction case.
The complex features of multi-reaction systems
are illustrated vividly by the experimental study of
Mike Harold [13] who measured the temperature of a
single catalytic pellet as a function of the ambient gas
temperature for the co-oxidation of carbon monoxide
and ethane in air. Figure 2 describes six experiments
carried out with mixtures having the same concentra-
tion of ethane but different concentrations of carbon
monoxide. At low CO concentrations (case a) the
bifurcation diagram of Tp vs. Tg consists of two dis-
tinct hysteresis loops; the first one corresponds to CO
oxidation and the second to ethane oxidation. Increas-
ing the CO concentration causes the two loops to over-
lap and creates rather complex behavior with up to
four different states at the same Tg (e.g., case c).
Moreover, in some cases an internal loop exists which
is completely nested within the external one (case d).
Clearly, this internal loop can be easily missed in an
experimental study unless one has some a priori guid-
ance about its existence.
A map of the operating conditions leading to differ-
ent numbers of solutions (Figure 3) shows that the
regions with four stable states is surrounded by five
distinct regions with three states. Each of these is

Tg (*C)
120 160 200 240 140 180 220 120 160 200

300- I I

200 i 4.8%CO
diI 4.1% C2,H
S*d. I e. ,*", ,f.
100 140 180 220 120 160 200 0 100 200
T (* C)

FIGURE 2. Bifurcation diagrams of pellet versus gas tem-
perature for the co-oxidation of ethane and carbon
monoxide on a single catalytic pellet [13].

surrounded by some with two solutions, which are in
contact with regions having a unique state.
The experiments clearly indicate that it is impor-
tant to have a rational and efficient scheme for
answering the following questions:
What is the maximum number of possible
solutions, and what is the number of solutions cor-
responding to a specific set of parameters?
What are the different types of bifurcation
diagrams and what type is obtained for a specific
set of parameters?
The large number of parameters which appear in
mathematical models of these systems renders im-
practical any attempt to answer these questions by a
numerical parametric study. Moreover, the traditional
ad-hoc mathematical methods used in the past are not
powerful enough to answer these questions.
About five years ago, my ex-graduate student and
current colleague, Vemuri Balakotaiah, suggested
that we attempt to answer these questions by use of
the catastrophe theory and the singularity theory with
a distinguished parameter. The application of these
techniques led to many interesting and powerful re-
sults. I shall attempt to describe briefly these two
mathematical tools, which are not familiar to most
chemical engineers, to illustrate their ability to yield
answers to the two questions posed above, and to com-
ment on future applications by chemical engineers.

The mathematical models of chemically reacting
systems are based on species and energy balances.
When the state variables are spatially uniform, such
as the concentrations in a CSTR, we define the reactor
to be a lumped-parameter system. The corresponding
steady state model is described by a set of algebraic

F(y,p) = 0

where y is a vector of n state variables (concentrations
and temperatures) and p is a vector of M parameters.
The state variables in distributed parameter systems
are position dependent, such as the concentration in a
packed-bed reactor, and the mathematical model is of
the form

F(y, Vy, V2y, p) = 0

where the Vy and V2y are associated with the convec-
tive and diffusive fluxes.
In many applications n-1 elements of y may be ex-
pressed as an explicit or implicit function of one of the



0 LO 2.0 3.0 4.0 5.0 6.0

FIGURE 3. A map of parameter regions with different
number of solutions for the co-oxidation of ethane and
carbon monoxide on a single catalytic pellet [13].
variables. These relations may be used to eliminate
n-1 variables so that the steady state is described by
a single equation. We restrict the discussion here to
such cases even though the mathematical theory can
handle the more general case.
We start with the analysis of the number of solu-
tions of a lumped parameter system described by the
single algebraic equation

F(y,p) = 0 (9)

We consider later distributed parameter systems.
One of the first teachings of elementary calculus is
that a local extremum exists typically at any point at
which the function and its first derivative vanish. The
type of the extremum point (maximum, minimum) de-
pends on the sign of the second derivative of f. When
the function and its first two derivatives vanish simul-
taneously a critical point is obtained. A natural follow-
up question is what are the features of a function next
to a singular point (yo, po) at which F (yo, po) vanishes
simultaneously with its first k derivatives, i.e.,

dF d2F = dkF = 0 (to)
dy dy2 dy

o (11)

We define such a critical (or singular) point to be
of codimension k. The catastrophe theory, which may

be considered to be a sophisticated extension of
elementary calculus, predicts that in the vicinity of a
singular point of codimension k the surface rep-
resented by the steady state equation (9) is qualita-
tively similar to that describing the polynomial
wk+1 = 0 (12)
i=0 ,
in the vicinity of the origin in the common situation
that rank (b) = k, where (bi) are elements of a k x M
matrix obtained from the series expansion

(y. (y0b. + h.o.t. (13)
i j=1

An important conclusion of this result is that F
must have k + 1 solutions in the vicinity of the singu-
lar point. Thus, one efficient way of looking for the
maximum number of solutions is to find the singular
points) of the highest codimension.
This simple technique enabled the finding of the
maximum number of solutions for a large number of
lumped parameter chemically reacting systems. For
example, Balakotaiah [14] considered the case of N
parallel independent, exothermic reactions

A. P.
1 1

i = 1,2,...,N

having identical and large activation energies. He was
able to prove that N! distinct singular points of
codimension 2N exist, i.e., there exist N! distinct
parameter regions having 2N+1 solutions. This im-
plies that for four parallel reactions, twenty-four sepa-
rate regions with nine solutions exist. Obviously, it
would be unreasonable to attempt to find these
parameter regions numerically without having a
proper theoretical guidance about their number and
The theory is only a local one and does not predict
the number of solutions in the global parameter space.
It does, however, give a lower bound on the maximal
number of solutions. For example, Hu [15, 16] found
in a study of a zeroth order reaction within a porous
catalytic pellet that up to five steady state solutions
exist even though the highest order singularity was
of codimension three (a swallowtail). Moreover, we
shall examine later a distributed parameter system,
which can have an arbitrarily large number of solu-
tions, even though the highest order singularity is of
codimension two (a cusp).
In applications it is important to know the number
of the solutions not only next to a singular point, but
for a specific set of parameters. In addition, one may


The previous examples were of systems
the steady state model of each is a single algebraic
equation .... in many applications the set of equations
describing the steady state cannot be reduced
explicitly to a single equation.

need to know the parameter values at which the
number of solutions changes, i.e., the structure of the
solutions. When F is continuous and there exists no
set of feasible parameters for which F vanishes on the
boundaries of the state variable, then the number of
solutions may change only when the parameters cross
the bifurcation set. This is the set of M parameters at

F(y,p) = F = 0 (15)

When the number of parameters is large, the con-
struction of this M-1 dimensional surface is very dif-
ficult. One may construct a two dimensional cross sec-
tion of the bifurcation set for specified values of M-2
parameters. However, this scheme does not enable an
efficient finding of the regions having the largest
number of solutions.
Br6cker and Lander [17] developed a method for
dividing the parameter space of a polynomial function
into regions having a different number of solutions.
This procedure requires constructing the locus of sin-
gular points of codimension k + 1 2m in the (p2m-1,
P2m) plane for m = 1,2,... For example, consider the

y5 ply3 p'y2 p3y P4 = 0

able (y; or yu). Crossing of this set is encountered in
many control problems and detailed analysis of such a
case is presented in [22].
Polynomial functions have only one singular point
of the highest codimension (k) and the loci of the sing-
ular points of codimension k-1 do not intersect at any
other point. Thus, any planar cross-section of the
bifurcation set has at most one region with k+1 solu-
tions. However, for non-polynomial equations several
singular points of codimension k may exist and the loci
of the singular points of codimension k-1 may intersect
in the (pl, P2) plane. Thus, a planar cross-section of
the bifurcation set may have several separated re-
gions with k+1 solutions. It is shown in [18] that such
a behavior occurs for example when two consecutive,
first-order, exothermic reactions are carried out in a
The previous examples were of systems the steady
state model of each is a single algebraic equation.
However, in many applications the set of equations
describing the steady state cannot be reduced
explicitly to a single equation. For example, consider
N(=-3) parallel, independent nth order reactions occur-
ring in a CSTR. The corresponding steady state equa-
tions are

q(Ci,f Ci) VkiCin = 0 i = 1,2,...,N

qpc (T Tf) + Ua(T T ) V (-AHi)kiCin


= 0


One starts by constructing in the (pl, P2) the locus of
the singular points of codimension 3 (swallowtail
points) (see Figure 4). One then selects a specific point
in that plane and constructs the corresponding locus
of singular points of codimension 1 (fold points). For
any (pi, P2) in region I (within the cusp) the (p3, p4)
is divided into three types of regions having either 1,
3 or 5 solutions (see Fig. 4). For any (pl, P2) in region
II (outside the cusp) the (ps, p4) plane contains two
types of regions having either one or three solutions.
This method can be applied also to predict the
structure of the solutions for non-polynomial equa-
tions and examples are presented in [18-21]. Two spe-
cial features may require a modification of the proce-
dure in such cases. The first is that when the state
variable is bounded (yl < y < Yu) the number of solu-
tions may change even when the parameters do not
cross a bifurcation set. This may occur when they
cross a boundary set, which is defined as the set of
the parameters for which the steady-state equation
has a solution on a feasible boundary of the state vari-

FIGURE 4. Locus of the swallowtail points in the (Pl, P2)
plane for Eq. (16) and cross sections of the bifurcation
set in the (ps, P4) plane for several (P1, P2) values. After
Brocker and Lander [17].


These equations cannot be reduced for most n into a
single steady state equation. However, they may still
be analyzed by the techniques described above after
application of the Liapunov-Schmidt reduction
method, which is explained in [20, 23].
The method of predicting the number of solutions
can also be applied directly to any system which is
described by an ordinary differential equation with
split boundary conditions. For example, consider the

v2Y s-) = f(y.p) (19)
ZsdI z

subject to the boundary conditions

aly(0) + a2 (0) = a

bly(1) + b2 (1) = b
2dcz -3

and the highest codimension of any singular point is
two (number of elements in p). Witmer found that for
a slab geometry a single cusp exists in the (K,(E)
plane. However, for both cylindrical and spherical pel-
lets an infinite number of nested cusps exist (see
schematic Fig. 5) so that for a bounded range of (
values an arbitrarily large number of solutions exists
for a sufficiently large adsorption coefficient. This
example illustrates the point that the number of solu-
tions in the global parameter space may exceed that
predicted from the codimension of the singular point.


(21) Lg(o)

If the value of y(0) is assumed then the differential
equation (19) can be integrated from z = 0 so that the
second boundary condition becomes a function of the
assumed y(0). Thus, any steady-state solution has to
satisfy the algebraic condition

F[y(O),p] = bly(1) + b2 (1) b3 = 0 (22)

The mathematical techniques developed previ-
ously for the analysis of an algebraic equation can
therefore be applied directly in this case. For exam-
ple, a bifurcation set has to satisfy Eq. (22) and
dF dq-(1)
F = b1q1(1) + b2 0 (23)

The value of qi = dy/dy(0) may be found by integrat-
ing the linear initial value problem

V2 q (24)

q1(0) = 1 (25)

dq(0O) al
dz a2

(a2 t 0)

Similarly, we can find singular points of higher
codimension. Witmer [21] used this scheme to find the
structure of the solutions of various reaction diffusion
problems. For example, he analyzed an isothermal
Langmuir-Hinshelwood reaction within a porous
catalytic pellet for which

f(y,p) = *2y/(l + Ky)2 (27)

FIGURE 5. A schematic of the cusps which divide the ((D,
K) plane into regions with different numbers of solutions
for an isothermal Langmuir-Hinshelwood reaction in a
cylindrical or spherical pellet [21].

It also points out the strong predictive power of the
A major advantage of the technique is that it en-
ables a complete prediction of the global structure of
the solutions of a model. This information can be
exploited to investigate a hierarchy of models of in-
creasing complexity and to evaluate the impact of the
various assumptions. For example, Hu [15, 16] re-
cently investigated the multiplicity features of a por-
ous catalytic pellet, the temperature of which is uni-
form but different from that of the surroundings, in
which a nth order reaction occurs. He found that ac-
counting for the intraparticle concentration gradients
introduced some surprising qualitative features,
which cannot be guessed from an analysis of the
lumped model. For example, five solutions exist only
if the reaction order is smaller than some critical
value. Moreover, the maximal number of possible sol-
utions depends on the shape of the pellet for certain
reaction orders. Such a systematic delineation of the
special features of a model is useful not only in analyz-
ing the behavior of chemically reacting systems but
also in many other areas.
Continued on page 52.


I views and opinions

Design, Accreditation, and

Computing Technology

University of California
Berkeley, CA 94720

TrHE ROLE OF DESIGN in the undergraduate chem-
Iical engineering curriculum has been the subject
of a great deal of emotional discussion; see, for exam-
ple, the article by James Wei in the summer, 1985
issue of CEE. Many chemical engineering educators
feel that the current AIChE/ABET accreditation re-
quirement of one-half year of design (i.e., 16 credits
in a 128 credit program) is excessive, and they resent
what they perceive to be an externally-imposed, edu-
cationally-unsound restriction on curricular develop-
ment. They point to the fact that holding to what they
consider to be an archaic emphasis on process design
in a crowded curriculum makes it difficult or impos-
sible to expose chemical engineering students to such
new, important areas of the profession as biotechnol-
, advanced materials, and solid state applications.
(This objection is most often enunciated by faculty
from research-oriented departments, who quite cor-
rectly observe that most curricular innovations dur-
ing the past three decades have come in areas that
c '" iwd the profession as new research fields having
no natiu, home in existing course structures.)
Few faculty, however, would object to the premise
that one-eighth of the undergraduate curriculum
should consist of coursework that is built around de-
veloping an appreciation for attacking and solving
open-ended problems. Indeed, most would argue that
such problem solving is the goal of an education in
engineering (and in science, if one is to draw arbi-
trary distinctions), and that a certain amount of
open-endedness should be a part of every chemical
engineering course. Where, then, is the problem?
The difficulty, it seems to me, is that hardly any-

Rather, it should be integrated throughout
the curriculum, with a "design" component in every
course. This is the educationally sound resolution
to the accreditation "constraint," . .

Copyright ChE Division ASEE 1986

body who is complaining about the "restrictive" design
requirement realizes that it is not a requirement to
teach one-half year of process design. Design, in the
context of accreditation, refers to the solution of open-
ended problems, which everyone accepts as an essen-
tial part of a chemical engineering education. Design
need not (and, with the exception of the single
capstone design course, should not) be singled out and
treated as something different from engineering sci-
ence. Rather, it should be integrated throughout the
curriculum, with a "design" component in every
course. This is the educationally sound resolution to
the accreditation "constraint," and it provides as
much room for innovation and new applications
areas as an innovative faculty can create.
The challenge, then, is to find the way to incorpo-
rate open-ended problem solving throughout the un-
dergraduate curriculum. This was admittedly dif-
ficult even a decade ago, but advances in computing
technology have created dramatic changes in our edu-
cational opportunities. Students now expect to use
computing technology in their courses, and are un-
doubtedly chagrined to discover that their archaic
mentors are unprepared to exploit their expectations
and abilities. What is needed is a real commitment
on the part of the teaching profession to develop integ-
rated lessons that enable students to explore the de-
sign implications of engineering science through
open-ended problem solving in all of their courses.
This kind of educational development is time-con-
suming, but worthwhile (particularly in the light of
the growing accreditation pressures regarding compu-
Now is the time to introduce the commercial mes-
sage. The following Position Paper represents the
start of an initiative by the CACHE Corporation to
assist chemical engineering departments with the ef-
fective integration of computing technology into the
undergraduate curriculum. This initiative is continu-
ing through the work of a Curriculum Task Force,
whose charge is to encourage the development and dis-
semination of curricular lessons using computing
technology in core undergraduate chemical engineer-
ing courses: stoichiometry, reaction engineering,
fluid mechanics, thermodynamics, mass transfer,


etc. One goal of this activity is to enable students to
acquire the skills defined in the Position Paper. There
is a second goal, which in my opinion can have much
farther-reaching consequences. A properly-oriented
set of lessons introducing open-ended problems into

the core courses will meet the accreditation "design"
objectives without cutting back on the content of these
courses in any way, opening the way for curricular
innovation within the constraints of a tight, four-year

Expectations of the Competence of

Chemical Engineering Graduates

in the Use of Computing Technology

A Brief Position Paper by


CHEMICAL ENGINEERING practice is now heavily
dependent on diverse applications of computing
technology. While specialized skills are required for
particular tasks, all chemical engineers can expect to
utilize certain areas of computing technology as a mat-
ter of course, and it is reasonable to expect certain
areas to be covered in depth in all bachelors-degree
curricula. The means by which such topics are incorpo-
rated in the curriculum will differ, depending on in-
stitutional traditions, strengths, and preferences, but
failure to include the areas discussed here in some
manner will result in a graduate who is ill-equipped to
practice the profession.

The uses of computing technology in chemical en-
gineering practice can be roughly classified into the
following categories:
scientific computation
text editing
data management and manipulation
data acquisition
While these categories are neither mutually exclu-
sive nor totally inclusive, they provide a useful per-
spective for curricular needs. The first three pertain
to computer software; computer speed and memory
are relevant here only with regard to scale, though it
can be anticipated that many applications will be car-
ried out on personal computers. A common need is
*Prepared by the CACHE Curriculum Subcommittee: Morton
M. Denn, Warren D. Seider, Co-Chairmen; H. Scott
Fogler, G. V. Reklaitis, Irven H. Rinard, Edward M. Rosen, Johr
H. Seinfeld.

Competence in a language implies not only
The ability to write scientific programs, but also a
sufficient understanding of programming logic to
test and adapt programs written by others.

familiarity with at least one of the standard operating
systems (UNIX, MDOS,....); it can be assumed that
a graduate thoroughly familiar with one operating sys-
tem can adapt to another as the need arises. We thus
conclude that a fundamental expectation is that the
chemical engineering graduate must be familiar with
at least one operating system for personal and main-
frame computers. Familiarity with an operating sys-
tem implies competence in file manipulation, text edit-
ing, graphic display, etc.
All chemical engineering graduates are currently
exposed to the elements of scientific computation,
though few receive sufficient reinforcement in under-
graduate coursework to ensure the necessary compe-
tence. "Fluency" is required in at least one of the
standard scientific programming languages (FOR-
TRAN, PASCAL, C,...); it can be assumed that an
individual competent in one of the scientific pro-
gramming languages can learn others as the need
arises. The chemical enqineerinq graduate must be
competent in the use of at least one scientific proqram-
ming language. Competence in a language implies not
only the ability to write scientific programs, but also
a sufficient understanding of programming logic to
test and adapt programs written by others.
Modern engineering practice is dependent on the
acquisition and processing of data through electronic
means. The practicing engineer must have a working
familiarity with the methods by which data are ac-
quired, transmitted, and recorded. The chemical en-
gineering graduate must have experience in the com-
puter-aided acquisition and processing of informa-


Most chemical engineering graduates make sur-
prisingly little use of library resources; for many, the
senior design project provides their first real exposure
to the engineering literature. Familiarity with modern
library resources is important and, hence, it is de-
sirable for each student to conduct at least one search
using information retrieval from electronic data bases
such as Chemical Abstracts Service and Scientific In-
formation Systems.
Word processors are achieving the "essential"
status of hand-held calculators. They are becoming
the principal vehicle for the generation of reports.
New computer-aided drafting packages are effective
for preparation of figures and, hence, it is desirable
for the chemical engineering graduate to have experi-
ence in the use of word processors and graphics pro-
grams for the generation of reports.
Many industrial organizations and university cam-
puses are utilizing networks of computers that share
common data bases. More and more, professional en-
gineers, faculty, and students are finding it advan-
tageous to communicate with external computers to
utilize electronic mail and data base facilities. Al-
though it is too early to require that all graduates
have experience with electronic mail and external
data bases, such a requirement should be feasible in
the next 2-5 years.

The basic skills defined here can be achieved only
if computing technology is integrated throughout the
curriculum. Students are required in most curricula
to write short programs of their own, and they are
often required to use programs supplied by others.
They are rarely asked to evaluate programs supplied
by others for efficiency, correctness in coding of the
equations and/or algorithms, or correctness of the un-
derlying equations/algorithms. It is important to rec-
ognize that the software selection is an important re-
sponsibility of many chemical engineering profession-
als, and students need experience in evaluating pro-
grams supplied by others as well as in their use. We
must teach how to perform an evaluation and verifica-
tion of programs supplied by others

Most scientific computation requires the solution
of algebraic or differential equations, maximization/
minimization, or statistical analysis. Chemical en-
gineering graduates should understand the principles
underlying such computation, including the bases
upon which typical algorithms are developed (numer-
ical methods). They should also have an appreciation

Data management and spreadsheet programs
are becoming increasingly important, and familiarity
with their use is desirable; spreadsheets are now
being used . for scientific calculations
such as material balances.

of concepts of numerical analysis such as convergence
and stability; the latter are rarely covered, but are
essential to the intelligent use of computational
Data management and spreadsheet programs are
becoming increasingly important, and familiarity with
their use is desirable; spreadsheets are now being
used in the chemical industry for scientific calculations
such as material balances.
Non-numeric programming is gaining importance
for rank-ordering, generating combinatorial alterna-
tives, implementing complex data structures, and for
analytical calculus. Increasingly, chemical engineering
graduates need to understand the principles of utiliz-
ing lists, queues, and pointers along with standard
numerical methods. These play a key role in artificial
intelligence and robotics and are increasingly being
applied in the synthesis and analysis of process flow-
sheets. Although not widely used in the under-
graduate curriculum, these structural problem-solv-
ing techniques are finding new applications.
Because of the increasing use of computer termi-
nals for communication, as well as for computation,
touch typing is a mechanical skill that should be en-

Integration of the skills defined here into a chem-
ical engineering curriculum can be carried out in
many ways. Familiarity with methods of data acqui-
sition is likely to be incorporated into a general labora-
tory course or as a laboratory associated with the
course in process control. Scientific programming and
the use of externally-supplied programs (FLOW-
TRAN, for example) is common in courses in design
and control, but the other core courses are under-
exploited and provide an opportunity to establish the
use of computational technology as a part of the nor-
mal "culture" of the graduate.
Furthermore, the effective use of computational
technology provides an opportunity for the introduc-
tion of open-ended problems at all levels of the core
curriculum; this is particularly relevant in view of the
need to maintain a minimum level of design (i.e.,
open-ended problems) in the curriculum for accredita-
tion purposes. []


|J5 Dbook reviews

By Thomas E. Daubert
McGraw-Hill Book Company, New York, 1985
pages xx, 469
Reviewed by
T. S. Storvick
University of Missouri-Columbia
When one reads this thermodynamics textbook,
the career of the author flashes by. Prof. Daubert
spent a major part of his career studying the ther-
modynamic properties of petroleum fluids. His recent
work on the API "Technical Data Book-Petroleum
Refining" and the AlChE Design Institute for Phys-
ical Properties sponsored "Data Prediction Manual" are
widely distributed and well-known. This textbook
tends to be a "how to" manual for these major works.
The general power of thermodynamic analysis and the
elegance of the mathematical structure of classical
thermodynamics are reduced by the apparent haste of
the author to move on to the details of the calculation
of the thermodynamic behavior of petroleum fluids.
The usual chapter headings we expect in a chemi-
cal engineering thermodynamics textbook are pre-
sented with a different ordering of the material. Start-
ing with a chapter on definitions and p.v.T. proper-
ties, Chapters 3 and 4 introduce the first and second
laws. Chapter 4 is an example of the ordering of ma-
terial that the author has chosen. Word statements of
the second law are quoted from ten sources followed
by the Clausius equality "AS = dQrev/T" [sic] (p. 99).
These four pages are followed at once by worked
examples calculating numerical values of the change
in entropy for ideal and nonideal gas systems, chemi-
cal reactions, and lost work process analysis. Then we
find Carnot cycle analysis, exergy analysis, the free
energy functions and the calculations of the ther-
modynamic properties (E, H, S, and G) using the ideal
gas and real gas equations of state and principle of
corresponding states correlations. This chapter ends
with analysis of thermal engine cycles and gas liquifac-
tion processes. This is truly an action-packed 90 pages
of textbook. From this summary, it appears that the
matrix of topics usually covered in a thermo textbook
is presented in columns rather than the rows as we
have come to expect from other textbooks.

The mathematical relationships among the ther-
modynamic variables are presented in Chapter 5 using
both the Bridgeman tables and Jacobian determin-
ants. Computation and construction of tables and
charts is covered in detail (about 30 pages). Chapter
6 presents correlations for estimation of ther-
modynamic parameters and properties (p, mol. wt.,
Tb, sat. vap. pressure, T., pe, ve, zc, wo and mixture
combining rules). Chapters 7 and 8 present physical
equilibria and the book concludes with a chapter on
chemical equilibrium.
Professor Daubert does accomplish his goal of pre-
senting procedures for solving problems of industrial
importance. The worked examples and exercises for
the student are generally drawn from hydrocarbon
processing and substances from fuel conversion pro-
cesses. The usual fluids, air and water are also used
with the number and variety of the problems adequate
for a textbook.
The presentation of the structure of ther-
modynamics is not as well accomplished. Using Chap-
ter 4 again as an example, the first sentence reads,
"The essence of thermodynamics is the second law and
its applications." That's reassuring to the reader!
Three pages later, when introducing the entropy func-
tion (4.2 Entropy, pg. 98) one finds the statement,
"Entropy is one of the most difficult concepts in ther-
modynamics for many to grasp as it is intangible and
cannot be measured calorimetrically or any other
way." This paragraph ends with the statement, "Full
proofs and derivations are beyond the scope of this
textbook; Denbigh (1981) gives the most lucid
analysis." This may be a self-fulfilling prophesy. When
an author says the material we're discussing is not
easy to explain so why don't you read it elsewhere,
the rush to get to the next application may lead to
careless statements.
One such statement occurs on page 4 where we
find, "Volume is the amount of three-dimensional
space occupied by a substance and is dependent on the
mass of material." Professor Daubert knows that vol-
ume is length cubed and has nothing to do with the
mass in that volume.
Another hurried definition occurs on page 130. "A
spontaneous process is simply a process which will
occur in some measurable amount of time either in an
isolated system or between a system and its surround-
ings as long as the surroundings have no effect on
the process." Given this definition, how does one ac-
Continued on page 38.




University of Wyoming
Laramie, WY 82071

THE QUESTION WHICH will be addressed in this
paper concerns the driving force for diffusive mass
transport. We will first consider the unidirectional dif-
fusion of a gas phase binary. It is commonplace to find
Fick's law written in terms of a gradient in component
mole fraction
A AB dz )

or a gradient in concentration
A = -PAB dz (2)

Another form, not so common, but nevertheless of
interest to our discussion is
A RT dT (3)
where PA is the component partial pressure. In these


Henry Haynes received his PhD in chemical engineering from the
University of Colorado in 1969. He was a research engineer at Esso
Research and Engineering in Baytown, Texas, from 1968 to 1971, and
was on the chemical engineering faculty at the University of Missis-
sippi from 1971 to 1982. Currently he is a professor of chemical en-
gineering at the University of Wyoming. Research interests include
heterogeneous reaction kinetics, chemical reactor design and synthetic
fuels from coal.

equations JA is the component A molar flux relative
to the molar average velocity. In terms of the molar
flux relative to stationary coordinates, NA, we have
the equivalent expressions

A = AB d + YA (NA + B

NA = -AB dZ + A A A + B)

A RT d + YA A B)

Clearly all three forms, Eqs. (1), (2) and (3) or Eqs.
(4), (5) and (6), are identical when the gas is ideal and
both temperature and pressure are constant. The
choice of driving force may be either the gradient in
mole fraction, concentration or partial pressure. For
isothermal, nonisobaric systems Eqs. (2) and (3) are
equivalent, but since the molar density is pressure
dependent, Eq. (1) is unique. Similarly Eqs. (1), (2)
and (3) are all unique when both pressure and temper-
ature are allowed to vary. Which form of the diffusion
equation is appropriate for use under such cir-
Most chemical engineering texts will write Fick's
law in terms of the gradient in mole fraction, Eqs. (1)
or (4). Skelland [1] points out that utilization of Eq.
(2) in a purely molecular diffusive process restricts
the system to constant pressure. Then in order to ob-
tain more general results he recommends usage of Eq.
(1). However, pressure gradients are generally estab-
lished by factors other than ordinary molecular diffu-
sion. Common examples include the effects of viscous
flow, external forces acting on individual molecules
and Knudsen diffusion. In the absence of such effects
there can be no gradient in pressure, and so there is
no contradiction in the restriction implied by Eq. (2).
The question of diffusive driving force is also ad-
dressed in the text by Sherwood, Pigford and Wilke
[2]. They too recommend usage of Eq. (1) for general
applications, and the following example is cited to sup-
port this contention: "A concentration gradient of oxy-
gen exists in air at 1 atm in the immediate vicinity of

Copyright ChE Division ASEE 1986


a hot radiator, since the air density varies with tem-
perature. Yet there is no gradient of mole fraction,
and no diffusion except a trivial flux due to thermal
diffusion. Eq. (2) indicates a finite diffusion flux, but
Eq. (1) does not." This argument eliminates Eq. (2)
for application to nonisothermal systems, but not Eq.
(3). The component partial pressure is also constant
in this example.

The kinetic theory of gases provides a powerful
and reliable means of treating diffusion in dilute gas
phase systems. The diffusion process has also been
treated in terms of irreversible thermodynamics, but
any useful results derived from this theory are redun-
dant.* Kinetic theory results are far more detailed.
Unfortunately the rigorous kinetic theory deriva-
tion of Fick's law is tedious, even when limited to
interactions between hard spheres. We shall therefore
employ an approximate kinetic theory known as the
momentum-transfer method [5]. Results obtained
from the momentum-transfer kinetic theory are gen-
erally of the same form as the more rigorous theory,
only the expressions obtained for the diffusion coef-
ficients may be off by a constant numerical factor.
Since we are interested primarily in the form of the
diffusion equation, the momentum-transfer kinetic
theory is adequate for our needs.
Consider a two-component gas contained in a tube
of radius, r, as illustrated in Figure 1. The procedure
will be to perform a z-momentum balance on molecules
of type A over the increment Az. Generally momen-
tum is exchanged by collision with other molecules
and by collision with the wall. Simple kinetic theory
provides the following familiar relations for the colli-
sion numbers

Z = alAB rB /8KT/_mF
AB = nAB

AS = nA A

where ZAB is the average number of collisions be-
tween unlike molecules per unit volume per unit time,
and ZAS is the average number of collisions of
molecules A with the surface per unit area per unit
time. The reduced mass, m*, and the mean molecular
speed, VA, are given by

*For a discussion of limitations on the thermodynamics of irreversi-
ble processes the reader is referred to Wei [3] and Cussler [4].

. the approximation enters into the momentum
transfer derivation. The product of two averages
(average number of collisions times average momentum
loss per collision) does not in general equal the
average of the product (average momentum loss).

mA + m(B

VA = /8KT/Trm.

Other quantities are defined in the notation.
After a collision -between two hard sphere
molecules, both molecules will leave with the center
of mass velocity on the average. Letting UA be the

--- z --- -

FIGURE 1. Momentum balance on gas phase binary.

z-component velocity of molecules (A) before the colli-
sion and u, be the z-component center of mass veloc-
ity, the average z-momentum loss experienced by
molecules (A) due to collision with molecules (B) is

PAB = mAuA mAc = A (uA u)

The center of mass velocity is

mAuA + m UB
c m + mB

and upon eliminating uc between these last two equa-
tions we have

PAB = m (UA UB)

It is assumed that molecules striking the wall are
reflected diffusely. Then on the average a molecule
which collides with the wall leaves with z-component
velocity, ud = 0. (Note that the u's are defined relative
to stationary coordinates.) The average z-momentum
loss by molecules (A) due to a collision with the surface
is therefore



(14) DV = rv
KA 4 A

Provided that no external forces are operative, a z-
component momentum balance can be written by re-
ference to Figure 1 as

AB PAB r2Az ZAS PAS 27rrAz

+ PA z r2 PA z+Az 7rr2 = 0
z z+Az

In the limit as Az 0 this equation becomes

SZAs PAS + Z PAB 0 (15)

Upon comparing these relations with
Eqs. 18 and 19, we see that the coefficients
obtained from the momentum-transfer derivation are
(as anticipated) off by a constant factor.

It is in writing this equation that the approxima-
tion enters into the momentum-transfer derivation.
The product of two averages (average number of col-
lisions times average momentum loss per collision)
does not in general equal the average of the product
(average momentum loss). Note also that we have not
imposed either constant temperature or constant
pressure. A more precise derivation would, however,
account for the fact that molecules leaving a high tem-
perature region possess on the average a higher velo-
city and therefore a higher momentum than molecules
transferred from a low temperature region. This ef-
fect results in a thermal diffusion flux which is usually
of secondary importance and can be neglected for our
Upon substitution for the Zij's and pj's from Eqs.
(7), (8), (11) and (14) we can write Eq. (15) as

dP, mAY
dP = (2 KT )(nA nAG) + mA A (16)


GA = nAUA (17)

is the molecular flux relative to stationary coordi-
nates. Now let us define approximate ordinary and
Knudsen diffusion coefficients according to

S = 7rKT/2m* (1/mr AB2) (18)

When these definitions are combined with Eq. (16) we


Now let


and substitute for GB in Eq. (20) to obtain

G = I/KT dP A (22)
S1 ayAdZ

Dividing by Avogadro's number converts the molecu-
lar flux, GA, into the molar flux, NA. Thus

N 1/RT dPA
A I -L 'A dz

a 1 +NA


Rigorous hard sphere kinetic theory provides slightly
different expressions for the ordinary diffusivity and
the Knudsen diffusivity

A KT/2m* (1/nf A )

KA = T rVA (26)
Upon comparing these relations with Eqs. (18) and
(19) we see that the coefficients obtained from the
momentum-transfer derivation are (as anticipated) off
by a constant factor. In subsequent discussion the
primed coefficients will be replaced with the more ac-
curate coefficients of Eqs. (25) and (26).
In large pores (r -. -) the Knudsen diffusivity term
disappears and Eq. (23) becomes
N dP
A RT(1 yA) dz (27)

which when combined with Eq. (24) can be rearranged


NA RT d A A +NB)

Thus, according to kinetic theory the appropriate
driving force for diffusion is the gradient in partial
pressure, i.e. Eq. (3). Use of Eq. (2) is therefore re-
stricted to constant temperature, and Eq. (1) is re-
stricted to constant temperature and pressure.
It is of interest to observe what may happen when
an incorrect form of the diffusion equation is applied.
The extension of Eq. (23) to multicomponent systems
can be written
I dP. N. v y.N. y.N.
-f = + ( 1 1 (28)
R Ki j=1 ij
Should we incorrectly take the driving force as a gra-
dient in mole fraction, the analogous equation is
dy. N. v y.N. y.N.
C dz + D.- (29)
z Ki j=1 ij
Schneider calculated the mutual concentration rela-
tions in a porous catalyst particle in which the hydro-
genolysis of cyclopropane was taking place in the gas
phase [6, 7]
cyclo C3H6 + H2 + C3H8

The diffusive mass transport was described by Eq.
(29). A very interesting plot taken from Schneider's
paper is reproduced in Figure 2. Here the sum of the
mole fractions over all components is plotted vs. the

Z 1.0 ,-- 0 A
0 ^83600 A
0 -
836 A




N 0.8
0 0.2 0.4 0.6 0.8 1.0

FIGURE 2. Sum of mole fractions corresponding to reac-
tant exhaustion. Cyclopropane hydrogenolysis [6].
(Reprinted by permission of Chemical Engineering Communica-
tions, 1 239 (1974)).


0 0.01 0.02 0.03 0.04

FIGURE 3. Pressure corresponding to reactant exhaus-
tion. Cyclopropane hydrogenolysis [8].

surface mole fraction of cyclopropane for several as-
sumed pore radii. In the large pore catalyst the mole
fractions sum to unity. However, the mole fractions
fail to sum to unity in the small pore catalysts, a result
clearly contrary to physical reality.
Schneider correctly points out that this inconsis-
tency in his calculation is due to gradients in total
pressure arising from a significant Knudsen diffusion
contribution in the small pore catalysts. However, he
does not identify usage of Eq. (29) as the source of the
inconsistency. The present author has reworked
Schneider's problem with the only change being to
replace Eq. (29) with Eq. (28) [8]. The computational
results are internally consistent, and Figure 3 re-
places Figure 2. As expected from the reaction
stoichiometry (2 moles 1 mole) the pressure de-
creases towards the interior of the small pore
catalysts. Despite the obvious inconsistency, the ap-
plication of Eq. (29) to problems of diffusion and reac-
tion in porous catalysts is still widely practiced.
If one connects two reservoirs containing gases of
different molecular weights by means of a fine capil-
lary or porous plug, a pressure difference will be es-
tablished between the two reservoirs due to the differ-
ent diffusive fluxes of the two gases. Alternatively,
one can adjust the pressure difference by means of a
side tube/piston arrangement to maintain a net zero
flux [9]. The appearance of this pressure difference,
usually referred to as the Kramers-Kistemaker effect,
provides another example of a nonisobaric diffusive
system. Assuming additivity, one can combine Eq.
(23) for the diffusive flux with the Poiseuille flow equa-
tion for the viscous flux to obtain an expression de-
scribing this phenomenon. The derivation is too
lengthy to present here, but the result is identical to
an equation derived by Mason et al [10], using the


dusty-gas theory. The success of this result, Eq. (71)
of Mason, et al, becomes evident upon consulting their
paper. The dusty gas theory is a highly detailed and
comprehensive theory of gas phase transport in por-
ous media. It is noted that the conclusion reached here
concerning the diffusive driving force in ideal gas
phase systems is consistent with dusty gas theory.

No theory of the liquid state has been developed
which approaches in predictive capability the kinetic
theory of the gaseous state. The only firm observation
upon which we can base our analysis is a result from
thermodynamics. It is well established that the cor-
rect driving force for diffusion is the gradient in chem-
ical potential. This is true for all forms of matter-gas,
liquid and solid. A general diffusion equation must
therefore conform to two requirements
1. The driving force must be a gradient in chemical potential.
2. The general equation must reduce to Eq. (3) in the ideal
gas limit.
An expression which has these properties is

CA dp
JA AB d(30)

for a binary, or
C. dp. n
S- = (y i- YiN)/Di (31)

for a multicomponent system.
Any textbook on solution thermodynamics can be
consulted for the relation between activity, aA, and
chemical potential.

PA =A + RT in aA (32)

dpA 1 dPA
dz CA dz

When Eq. (34) is substituted into Eq. (30) one obtains
Eq. (3) immediately. Thus both of our stipulations are
satisfied by Eq. (30).
Equation (30) can be written in a more convenient
form for application to liquids. Again differentiating
Eq. (32) at constant temperature we obtain

dp d in aA d in aA d An xA
RT dz RT dz

dA RT (d in aA) dxA
dz X A d n dz

Upon substitution for the gradient in Eq. (30) we have

Ad n aA dxA
JA C AB td en XA dz


The activity coefficient is now introduced through the
relation fA = AXAfA', and therefore

A f


Both fA' and fA0 are pure component liquid state
fugacities at system temperature; fA' is at the system
pressure and fA is at the standard state pressure.
The effect of pressure on liquid state fugacities is gen-
erally quite small so that to a very good approximation


and the component activity is given by

aA = fA/f

In these equations PA is the standard state chemical
potential, a function of temperature only; fA is the
standard state fugacity at system temperature and
specified pressure, and fA is the fugacity of component
A in the mixture at system temperature and pressure.
It is easily demonstrated that Eq. (30) reduces to
Eq. (3) in the ideal gas limit. For an ideal gas mixture
fA= PA and differentiating Eq. (32) at constant tem-
perature provides
dv A d in PA RT dPA
dz T dz PA dz


Zn aA = kn xA + kn YA

d n aA d in YA
d in xA + d n xA

Substituting into Eq. (36)

S= CD 1 + d in yAl dxA
A AB d n x Aj dz

It is emphasized that this equation is intended for use
with liquids only. The simplification of Eq. (38) does


not apply to gases since gas phase fugacities
strong functions of pressure. Equation (40) simple
further for application to ideal solution liquids (-YA=
JA AB dz



Thus the appropriate driving force for use with liquids
is the gradient in mole fraction. This is a consequence
of the equivalence of mole fraction and activity in ideal
solution liquids, Eq. (38). For a similar reason the
gradient in partial pressure arises naturally as a driv-
ing force for diffusion in ideal gas phase systems.
Kinetic theory predicts that the binary diffusivity,
DAB, is practically independent of composition in di-
lute gas phase systems, and this is confirmed by ex-
periment. In liquid phase systems the diffusivity is
generally found to be a strong function of concentra-
tion. Application of the well known thermodynamic
factor of Eq. (39) reduces the composition dependency
in most liquid phase systems (e.g. 11), but even dif-
fusivities in ideal solution liquids typically exhibit a
concentration dependence.

Current chemical engineering texts either imply
or explicitly teach that the driving force for diffusive
mass transport in ideal solutions is the gradient in
mole fraction. This is only true for ideal solution liq-
uids. An argument based on the kinetic theory of
gases has shown that the appropriate driving force for
use with ideal gases is the gradient in partial pressure.
The Kramers-Kistemaker effect is successfully de-
scribed by taking the driving force as the gradient in
partial pressure (or equivalently, the gradient in con-
centration since the system is isothermal). When one
incorrectly formulates a nonisobaric gas phase diffu-
sion problem in terms of the mole fraction driving
force, inconsistencies become evident. In the example
quoted the mole fractions did not sum to unity.
The general formulation of diffusive mass trans-
port, applicable to all mixtures-gas, liquid, solid,
ideal or nonideal-is of course based on the chemical
potential driving force. In the ideal gas limit, the gen-
eral formulation reduces to a Fick's law form which
has as its driving force the gradient in partial pres-
sure. For liquids, the general formulation can be writ-
ten in terms of a Fick's law form with mole fraction
driving force and a thermodynamic correction factor.


a, = Component i activity.
C = Molar density.
Ci = Component i concentration.
Di = Ordinary diffusivity.

Dm =
fi' =

fi =
Ji =
mi =
m* =-
n =
Ni =
Pi =
Pi =

Knudsen diffusivity.
Approximate ordinary diffusivity, Eq. (18).
Approximate Knudsen diffusivity, Eq. (19).
Component i fugacity in its pure state.
Standard state component i fugacity.
Component i fugacity in mixture.
Molar flux relative to molar average velocity.
Component i molecular mass.
Reduced molecular mass.
Molecular density.
Molar flux relative to stationary coordinates.
Average z-momentum loss of component i due
to collision with component j.
Gas constant.
Average center of mass velocity in z-direction.
Average velocity of reflected molecule in
Average component i velocity in z-direction.
Component i molecular speed.
Component i mole fraction (liquid phase).
Component i mole fraction (gas phase).
Axial length coordinate.
Collision number between species i and j.
Flux ratio parameter, Eq. (21).
Boltzmann's constant.
Component i chemical potential.
Standard state component i chemical potential.
Number of components.
Collision diameter.

1. Skelland, A. H. P., Diffusional Mass Transfer, Wiley, New
York, 1974.
2. Sherwood, T. K., R. L. Pigford, and C. R. Wilke, Mass Trans-
fer, McGraw-Hill, New York, 1975.
3. Wei, J., "Irreversible Thermodynamics in Engineering," Ind.
Eng. Chem. 58, 55 (1966).
4. Cussler, E. L., Multicomponent Diffusion, Elsevier, Amster-
dam, 1976.
5. Present, R. D., Kinetic Theory of Gases, McGraw-Hill, New
York, 1958.
6. Schneider, P., "Mutual Concentration Relations during Reac-
tion in Porous Catalysts in the Transition Region of Diffusion,"
Chem. Eng. Commun., 1, 239 (1974).
7. Schneider, P., "Intraparticle Diffusion in Multicomponent
Catalytic Reactors," Catal. Rev.-Sci. Eng., 12, 201 (1976).
8. Haynes, H. W. Jr., "Calculations of Gas Phase Diffusion and
Reaction in Heterogeneous Catalysts. The Importance of Vis-
cous Flow," Can. J. Chem. Engr., 56, 582 (1978).
9. McCarty, K. P. and E. A. Mason, "Kirkendall Effect in Gase-
ous Diffusion," Phys. Fluids 3, 908 (1960).
10. Mason, E. A., A. P. Malinauskas, and R. B. Evans, III, "Flow
and Diffusion of Gases in Porous Media," J. Chem. Phys. 46,
3199 (1967).
11. Vignes, A., "Diffusion in Binary Solutions," Ind. Eng. Chem.,
Fund., 5, 189 (1966). Dl




McMaster University
Hamilton, Ontario, Canada

A UTILITY BUILDING is located on most campuses.
It may provide steam, chilled water, compressed
air, emergency power, or waste water treatment
facilities. Indeed, right close by could be superb work-
ing examples of boilers, turbines, pumps, heat exchan-
gers, Ljungstrom heaters, ion exchangers, compres-
sors, cooling towers, and process control loops. That's
what we found when we "discovered" our campus
utilities plant.


This facility has six refrigeration units for the Uni-
versity-Hospital chilled water system, five steam boil-
ers, eight cell cooling towers and three air compres-
sors. The refrigeration units are
two 500 ton units handling about 45 L/s each (700 US
gpm) using refrigerant R-11
two 2000 ton units handling about 160 L/s each (2500 US
gpm) using R-114
two 5000 ton units handling about 450 L/s each (7000 US
gpm) using R-22

The chilled water enters the freon chiller at llC
(52F) and leaves at 4.5C (400F). The refrigerant is
condensed with cooling tower water.
Steam is produced at 1480 kPa (200 psig) with
about 55'C (100F) superheat at the drum. About 70%
of the condensate returns so there is 30% to be
supplied as fresh boiler feed. The city water is ion
exchanged for both anion and cation, and deaerated.
The furnaces are now gas fired, although some
facilities for handling Bunker C fuel remain. The
capacities are
one at 25 kg water evap/s (200,000 lb/h)
one at 19 kg water evap/s (150,000 lb/h)
two at 6 kg water evap/s (50,000 lb/h)
one at 3 kg water evap/s (25,000 lb/h)

*Paper 60a presented at the AIChE Annual Meeting,
Nov. 28, 1984, San Francisco.

The main components of the course
are to learn how simulators work and to
learn how to write computer programs to describe
the operation of heat exchangers, fluid handling
equipment, reactors, and separators.

Things To Look for On a Boiler House Visit
Variation in size of drives of centrifugal compressors.
5000 HP largest.
Notice insulation, size of it, type
Lubrication systems
Piping layout
Trace lines
why horizontal?
why lines?
study startup shutdown
considerations (pump out of H/E)

Why is cooling water green?
biocide added slugwise/week. dilute acid (to prevent
biological growth).
Sulfuric Acid storage room
how does acid come in?
Why raised floor?
Why safety shower?
How to maintain pump
Notice schedule 80 piping.
Pulsation dampener on exit of diaphragm pump.
Explain how cooling towers work
Induced draft, forced draft, natural convection.
This is induced.
Problems: liquid distribution, no recycle of exhaust

A thermal wheel or Ljungstrom heater is used for
heat recovery. The air compressors are two stage re-
ciprocating compressors.

Sophomores are introduced to individual items of
hardware through our "travelling circus" program.
Here they handle and study, on their own, about fif-
C Copyright ChE Division, ASEE, 1986


teen hardware items every two weeks until they are
familiar with about seventy-five items such as fittings,
meters, instruments, valves, and small processing
equipment. Details are given elsewhere [2,3].
However, the program does not give them an ap-
preciation of how a system works. How does it all fit
together? Sophomores are given a two-hour tour of
the boiler house in which particular attention is paid to
showing them ideas introduced in the mass and energy
balance course: heat of compression, cooling towers,
need for blowdown and purge from the cooling tower
posing other interesting ideas that they should think
Table 1 lists some of the things they should look for.
To help them keep track of the things seen we provide
example questions and places to record information.
This activity is one tutorial in the sophomore Mass
and Energy Balance course or as part of a problem
solving course.

As a result of a recent reorganization of our under-
graduate curriculum we have introduced a course in
computer simulation into the second semester of the
junior year. The main motivation for this course is to
take the teaching of simulation (and the accompanying
instructions on the use of .computer executives) out of
the senior year design project and to deal with it sepa-
rately. This allows the students more time to under-
stand how a simulator works and to gain experience

on small problems. Then, in the senior design course
they can concentrate on the design and optimization
of a much larger chemical process.
The executive program used to do detailed steady-
state simulations is GEMCS, a program developed at
McMaster University in the 1960's. Although many
newer, more complete executive programs have ap-
peared on the market (such as ASPEN, FLOW-
TRAN, PROCESS), GEMCS remains a good choice
for the classroom because it is very simple to use.
GEMCS is a sequential modular simulator. This sim-
ply means that a computer program (module) which
mathematically describes the operation of a piece of
equipment must be available to the executive program
for each process unit of the plant being simulated.
The main components of the course are to learn
how simulators work and to learn how to write com-
puter programs to describe the operation of heat ex-
changers, fluid handling equipment, reactors, and
separators. Such programs take in temperatures,
pressures, and flow rates of the incoming streams and
compute the output values in a form compatible with
the executive program. The degree of sophistication
of these modules can be large. For example, an overall
heat transfer coefficient can simply be inputted into a
module as a parameter or in a detailed module it can
be computed from fundamentals and the flow rates,
correlations and physical property data. Deciding on
the level of complexity appropriate for a particular
unit is an important decision to make in a simulation
As a large project in the simulation course we de-
cided to simulate the behaviour of each of the refriger-

Don Woods is a professor in the department of chemical engineer-
ing at McMaster University. He is a graduate of Queen's University
and the University of Wisconsin. His teaching and research interests
are in surface phenomena, plant design, cost estimation, and develop-
ing problem solving skills. (L)
Phil Wood is an associate professor of ChE. He has degrees from

the University of Waterloo and Caltech and was previously on the
faculty at Michigan State University. His research interest is in the area
of turbulent transport phenomena, especially mixing and mathemati-
cal modeling. (C)
Floyd Gallinger is the Chief Operating Engineer of the Physical
Plant at McMaster University. (R)


ation units in the boiler house. Figure 1 shows the
layout and a unit, and the details of the assignment
are given in Table 2. A schematic diagram of the freon
circuit simulated is shown in Figure 2. For this oper-
ation, the load the university puts on the circuit was
provided as input, as was the chilled water tempera-
ture supplied (40F). The cooling tower was not mod-
elled although this could be attempted in future years.
The choice of the refrigeration plant as the process
to be simulated proved to be a particularly good one
for the following reasons.

It only involved the principles of heat-transfer, fluid
flow and thermodynamics, all of which had been previ-
ously studied. At this point the students were taking
mass transfer and reaction engineering simultaneously
with this course. Hence, simulating a typical chemical
plant would have been too difficult.
The real pieces of equipment could be visited, touched,
and seen easily and frequently throughout the term.
The operating engineers at the boiler house kept de-
tailed log sheets of temperature and pressure for all of
the streams on both the freon and cooling water cir-
cuits, and they were available to answer questions.
Much information about each piece of equipment was
available from the manufacturer, along with the origi-



FIGURE 1. Layout of the 5000 ton refrigeration unit. The
condenser is the white heat exchanger on top and the
chiller is the black insulated heat exchanger on the bot-

nal design specifications which included such things as
the number of tubes, their diameter and length, and the
compressor motor horsepower.
0 Good thermodynamic data were available for R-11, R-22
and R-114, which were the refrigerants used in the vari-
ous units. Furthermore, correlations had been fitted to
these data so that a thermodynamics package could be
developed. (It should be noted that obtaining accurate
physical property data is often the major limitation to
good simulations.)

The students were divided into teams of seven for
the project and worked on it for about five weeks.
Initially they made a visit to the boiler house to see

Computer Simulation of a Refrigeration Plant

Call the university water, chilled water = CW and its temper-
ature Tcw so that we have a Tcw| and Tcwo. Call the cooling
tower water CT so we have TCT. and TCT.
Assume that Tcw. = 40F. To determine the load, you need
the flowrate and Tcw,; assume these are given. Also assume that
the cooling tower water supply rate and temperature are given.
(a) Simulate the refrigeration process for the design load (5000
tons, or 2000 tons) and the designed cooling tower water
flow rate and temperature. Use the actual heat transfer
coefficients calculated from the log sheet, not the designed
values. The output should be: (i) the coefficient of perfor-
mance (COP), (ii) motor horsepower = > amps drawn, (iii)
the CT water outlet temperature.
(b) Simulate the process for 75% load and 85F CT water inlet
temperature (effect of load changes).
(c) Simulate the process for 100% load and 75F CT water inlet
temperature (effect of cooling tower water availability).
(d) Simulate the process conditions corresponding to one hour
on your log sheet, say 2:00 p.m.
Food for thought the extra mile: Repeat part (a) but use
R-12 to see if this would improve the COP or horsepower

Condensing temperature = 104.7F
Condenser water in = 86F
Condenser water out = 95.4F
Condenser water flow rate = 6000 U.S. gal per min.
Condenser has 1839 tubes in 2 passes
Tubes are 3/4 inch 0.D. copper with low fins
12' 8" long
Surface ratio = 3.41
Inside diameter = 0.554 in.
Outside area = 11,200 ft2

Evaporating temperature = 32.8F
Chilled water in = 59F
Chilled water out = 39F
Flow rate = 2340 US gal/min.
Chiller has 1485 tubes in 3 passes
Tubes are same as condenser but Ao
Designed fouling factor = 0.0005
Motor horsepower = 1980 BHP

10,880 ft2


On the last day of the term groups
gave an oral presentation of their results . .
The results varied from a simulation which would not
converge to an excellent report which
considered eight additional cases.


FIGURE 2. Process flowsheet for the refrigeration plant
showing units which require modelling.

the equipment and to obtain as much information as
possible about each piece. This included such things
as matching the temperatures and pressures reported
on the log sheet to the physical location of where the
measurement was taken, the type of instrument, etc.
The large groups were broken into smaller ones (1-2
people) for the modeling of each unit in the plant (com-
pressor, condenser, etc.). Their first model was to be
simple so that the entire simulation could begin as
soon as possible. Typically, one person was in charge
of this job. Then as more detailed models became
available they were substituted for the early versions.
It is noteworthy that a time management program
(Critical Path Method) was discussed during the tuto-
rials for this course. Groups were advised to deter-

Results of Simulation of 2000 Ton Refrigeration Unit
Input from Log Sheets
Load = 1350 Tons, TCT,!n = 78F, Tcw,., = 40F

Pressure in condenser, psia
Condensing temperature, F
Condenser water outlet temp.,
Amps drawn by compressor




Data (from Log)


127 125

4.6 (Carnot COP = 9.5)

The Boiler House Project for Seniors

As part of your training program, today you will be visiting
our boiler house. During the next 3 tutorials you will have sev-
eral tasks to do:

1. See piping layout and equipment placement in practice.
Take one small section of the plant; draw a sketch of the
section and show the placement of the equipment and the
layout of the piping, valves, etc. Comment specifically on
the good and bad features of the part you looked at.

2. Calculate/estimate one of the following:

a. the boiler efficiency
b. the C.O.P. of the refrigeration unit.
c. the efficiency of a steam driven pump system.
d. the overall heat transfer coefficient in a shell and
tube exchanger.

For this activity, the following procedure should be followed:

(i) set up an algorithm of how you are going to do the
(ii) state how you will go about collecting the data you
need to do the calculations:

data from records?
data from instruments in the control room?
3. Identify a control loop on the system.

what type of control is used?
open loop, closed loop, feed forward, cascade?
what type of controller is used?
locate the controller, the measurement element
and the control elements.
what settings are used on the controller?

mine the critical path for a successful completion of
their project. Group skills and other problem solving
attributes were also introduced as part of this course.
On the last day of the term groups gave an oral
presentation of their results. A single report was also
required from each group. The results varied from a
simulation which would not converge to an excellent
report which considered eight additional cases. The
operation of a refrigeration plant could be very accu-
rately simulated as shown in Table 3.


The boiler house provides a unique opportunity for
sorting out process lines, considering plant layout, cal-
culating performance, and interacting with operators.
To exploit this opportunity, we have a 6 to 8 h boiler
house project. The project, given in Table 4, has three
components: equipment layout, calculation of perfor-
Continued on page 56.


I P a classroom



A Matter of Chemical Engineering

University of California
Berkeley, CA 94720

IF ANY PLACE IS more performance-oriented than
academia, it is the professional world that senior
students in chemical engineering are about to enter.
There, the ability to communicate is crucial; in fact, it
can be said that there is a direct correlation between
professional advancement and the ability to write and
speak effectively.
However, many of our chemical engineering stu-
dents, native as well as foreign born, are weak in ver-
bal skills. In their senior year they must write reports
and make oral presentations for the unit operations
laboratory. They must cope with verbal tasks for
which they have not been adequately prepared
throughout their years of schooling, freshman writing
requirements notwithstanding.
To meet that need, the department of chemical en-
gineering at the University of California, Berkeley,
established an in-house course, "Technical Communi-
cation." A prerequisite to the senior laboratory
course, it is given every semester to about fifty stu-
dents who are divided into three sections and graded
on a pass/not pass basis. The only route to exemption
is an optional exam that only about two percent pass.
In addition, the instructors offer a departmental con-
sulting service used mainly by students writing re-
ports for the unit operations laboratory. Now in its
seventh year, the program is staffed by three experi-
enced teachers who have made technical communica-
tion their specialty.
The course ranks high in student evaluations, and
faculty are pleased with the improvement in student

Part of its success is attributable to the
fact that the course is in-house,changing in response
to departmental needs; it functions as a de facto
statement to students that communication is
an important aspect of [their] work.

@Copyright ChE Division ASEE 1986


Ralda Sullivan has been in charge of an in-house program in tech-
nical communication for the Department of Chemical Engineering at
the University of California, Berkeley, since 1981. She received her
B.A. from Stanford University and her Ph.D. from the University of
California, Berkeley. Dr. Sullivan has taught writing and speech in a
variety of settings; currently, she lectures and consults on communica-
tion issues.
writing and oral presentations. Part of its success is
attributable to the fact that the course is in-house,
changing in response to departmental needs; it func-
tions as a de facto statement to students that com-
munication is an important aspect of a chemical en-
gineer's work.
Because there is so much to learn in one semester,
the course must necessarily be intensive. In structur-
ing the course, we use as a guide the demands of the
professional world. First, we try to establish a context
that realistically reflects the web of attitudes, expec-
tations, and practices which our students will en-
counter as chemical engineers. Second, we design as-
signments that teach multiple communication skills;
then we arrange these assignments in a sequence that
reinforces earlier learning and gives students a sense
of progress. Third, through self and peer evaluation,
students learn to monitor their own performances.

We have found that even students who are rela-
tively competent writers need guidance in making the


change from writing essays for college courses to writ-
ing reports for supervisors and clients. Although we
teach basic principles of effective discourse, our stu-
dents learn the difference between discourse as self-
expression and discourse for professional purposes.
Not only must they speak or write with a specific au-
dience in mind, but they must regard themselves as
decision makers writing for supervisors or clients.
They must stop thinking of themselves as under-
graduates writing for professors who know more than
they do. As they analyze the audience for each written
or spoken assignment, they learn to make appropriate
adjustments in diction and tone; this is one way in
which they begin to think of themselves as engineers
rather than students.
We also work to help students develop the at-
titudes of the professional. They must come to see
that, although writing and speech may be self-reveal-
ing, when they communicate in professional stitua-
tions, their purpose is to deliver a product for others
to use. The attitude we take toward revision of stu-
dent writing, for instance, is in keeping with the idea
that in industry one can learn from mistakes, but mis-
takes must be corrected. Therefore, a student can ex-
pect to revise a paper more than once-not because
he has failed-but because it is a necessary part of
doing a good job.
As engineers, our students must learn to perform
specific communication tasks: to write memos, letters,
and reports, to condense and paraphrase information,
to give clear explanations and instructions, to argue
persuasively, and to present complex material
through tables and graphs. They also must assess au-
dience and alter each presentation accordingly, write
under pressure, meet deadlines, and edit their own
writing as well as that of others. In addition, since
communication is oral as well as written, they must
learn something about negotiation, interviewing, and
group discussion as well as the delivery of formal pre-
sentations. Therefore, speech is integrated into al-
most every assignment.
Assignments usually take the form of cases based
on situations our students are likely to encounter on
the job. In each case, the communicator's role is de-
fined and the audience specified. For instance, an as-
signment may ask them, as process engineers in a
company that manufactures refrigeration equipment,
to write a memo for the sales staff explaining how a
home refrigerator works. They must explain what
happens at each stage of the process in terms under-
standable to college-educated graduates in business
administration. And always, since the business world
runs within constraints, there is a word limit and a


Assignments usually take the form of cases based on
situations our students are likely to
encounter on the job.


We must begin at the level where we find the stu-
dent and where he finds himself. Most students come
to us with no understanding of what is involved in
producing competent writing. It is, therefore, impor-
tant to demystify the process so that students come
to see that producing clear prose is hard but manage-
able work.
For the first paper, a technical description, we
walk them through the process by breaking it down
into steps (planning, first draft, editing, second draft,
editing, third draft). For this assignment, students
must first bring to class an outline and a rough draft;
these are edited and commented upon by classmates
in a workshop session, with the teacher acting as a
consultant. Students then incorporate the comments
and reactions of others into another draft. They learn
that they have to exercise judgment about what to
accept and what to reject. Finally, they turn in all
drafts and outlines along with a self-evaluative state-
ment about what major problems were encountered
in producing the paper. After the teacher reacts and,
if necessary, calls a conference, the student rewrites
the paper. On subsequent papers, the teacher
applauds progress but insists upon page-editing or re-
vision of problem passages, or even the entire paper,
when necessary.
To provide maximum exposure to various aspects
of communication, each assignment is layered with
multiple tasks-reading (research), speaking, listen-
ing, writing, and editing. For example, an assignment
in technical description requires each student to re-
search and orally describe a process or mechanism to
a teammate who is then obliged to write the descrip-
tion on the basis of what is learned from the partner.
Then they reverse roles with the teammate present-
ing a different technical process. Each, in the role of
speaker, must do research and then present the infor-
mation clearly; each as writer must listen carefully
and ask questions in order to produce a clearly written
explanation of causal principles.
At the next class session, each speaker is given
the task of editing the paper the teammate wrote. In
this way, each student sees the oral explanation mir-
rored back in the writing of a peer. Thus, in practicing
editing and self-evaluation before the teacher sees the
papers, students act again as if they are professionals.
In addition to layering each assignment so that

multiple tasks are performed, we arrange them in se-
quences to reinforce learning; in these sequences key
tasks are repeated in varying forms. For instance, in
writing abstracts, most students need several tries
before they perform well. The first exercise in con-
densing and paraphrasing is done in class. For exam-
ple, we read a short speech delivered by an industrial
leader on what constitutes an educated person. Then
each of us, teacher as well as students, condenses the
first two paragraphs into one sentence. After listening
to several attempts read aloud, we discuss strategies
for discriminating between key points and incidental
Next, the student, understanding that his task is
to distinguish major from minor points, is asked to
outline an article about four pages long. In this assign-
ment, the student is given further instruction in out-
lining as well as in summarizing. He brings his outline
of the article to class where, warned in advance, he
must test its value by writing within a time limit (say
twenty minutes) a summary of the main ideas. This
early try at writing an abstract or a summary also
gives the students the experience of writing under
pressure, something they will have to do on the job.
Such pressure smokes out weaknesses, alerting both
student and teacher to spelling, grammatical, and or-
ganizational problems that can be covered up when
the student takes more time-or gets help-outside
of class.
The next assignment in writing the abstract is
combined with the first lesson in argumentation.
From time to time, every chemical engineer must be-
come an advocate. As an example of effective advo-
cacy, we assign a brief persuasive article by an execu-
tive in a major chemical corporation. Students outline
main points and express the gist of the argument in
condensed and paraphrased form. In addition, they
must read critically in order to analyze the argument.
Because it is well written, we also use the article to
demonstrate paragraph coherence and emphasis. Fol-
lowing this, we move on to more work on advocacy,
but abstracting is not dropped. It becomes a part of
other assignments, particularly in written reports, for
every report must have an abstract or summary.
Pace is an important factor in giving students the
sense that they are making progress. We take care to
give students enough work to keep them stimulated,
but not so much that they are overwhelmed. We vary
types of assignments: speech is alternated with writ-
ing, technical description is followed by business cor-
respondence, a series of short exercises by a long re-
port. The course culminates in a written report of the
kind students will encounter in the unit operations
laboratory the next semester.

From the beginning we set high standards for
writing, and revising. However, to show that com-
petent writing is within the grasp-albeit with ef-
fort-of most students, we usually choose as models
the work of students, professional engineers, execu-
tives, and professors. Students are expected to
evaluate the spoken and written communication of
peers, guest speakers, and the writing staff. That
means they scrutinize attainable models.
Because feedback is essential to improvement, it
is structured into assignments. For instance, in
speech activities we use the video camera as well as
written comments by teacher and peers. Our students
are video-taped about four times during the semester
with playback sessions in class; students can then also
arrange for private viewings of their taped talks. The
difference between first and last performances in a
semester is dramatic.

Gradually we increase the demand on student pow-
ers of self-perception, encouraging them to recognize
successes, as well as difficulties. For instance, a shy
student might celebrate that he actually stood up in
front of a group and spoke coherently for two minutes;
another student might recognize that he now knows
the relationship between punctuation and meaning;
yet another, that he now understands how to go about
organizing a report. In such ways, the student experi-
ences positive gains he may have otherwise over-
looked, and the teacher finds out who tends to be
overly self-critical, who to be quick at self-congratula-
Because the course is designed to change behavior,
the teachers work to help the students realize that
while the burden of taking initiatives and making
progress is on them, they can turn for help and sup-
port to teacher and classmates in their roles as consul-
The teacher must manage the course material for
each student, as well as for the group, making modifi-
cations to facilitate each one's development. The ele-
ments combine in complex ways, a matter of class-
room chemistry, with the teacher observing and guid-
ing the reactions. Perhaps the term, chemical en-
gineering, can be used metaphorically to describe
what we do.
The teacher, besides being a motivator and consul-
tant to budding executives, models attitudes towards
communication: business-like yet human, holding high
standards yet spurring students to do what they can
at whatever level they can. In regard to his own writ-
ing and speaking, the teacher should be frank about
his difficulties with the process, inviting students to


criticize his communication. He also works collabora-
tively with students on some assignments, de-
monstrating how to take, as well as to give, criticism.
Above all, the teacher demystifies communication.
Lucidity becomes not a magical property given to
some and withheld from others, but the end result of
a process, subject to human frailty yet responsive to
effort. FD

book reviews

by Stanley M. Walas
Butterworth Publishers, Boston,
671 pages, $49.95 (1985)
Reviewed by
Wallace B. Whiting
West Virginia University
Hundreds of thermodynamics textbooks have been
written, and new volumes appear every month. So
why do we need another one? Certainly it is because
chemical engineers (and others) need to understand
thermodynamics, especially for use in determining
phase equilibria, and because thermodynamics is a dif-
ficult subject to explain. Dr. Walas avoids the pitfalls
common to other thermodynamics texts by limiting
the scope of his book; he does not attempt to explain
the basis of phase equilibria in terms of the First and
Second Laws, but rather he assumes that the reader
has studied (and learned) these concepts and is ready
for the design calculations for phase equilibria. This is
not a book that could be considered as the sole text
for the traditional one or two required courses in ther-
modynamics that are common in BSChe curricula in
the U.S. Rather it is a textbook for an advanced un-
dergraduate or graduate course specifically for design
calculations in phase equilibria. However, it lacks the
theoretical rigor common in textbooks aimed at this
audience-this could be seen as either an advantage
or a disadvantage, depending on one's point of view.
Perhaps the best audience for this book is the practic-
ing chemical engineer who remembers some ther-
modynamics and needs to come up to speed quickly in
phase equilibria.
Besides extensive coverage of the standard phase-
equilibrium topics, Walas has included many topics of
importance to chemical engineers that are often lack-
ing in similar texts. For example, there are sections
on gas hydrates, liquid crystals, critical phenomena,
supercritical equilibria, solid/liquid equilibria, and,
perhaps most important, a section on recommenda-

tions as to which 'of the many available correlations
one should use for a specific system. His description
of the relevant literature (especially the review litera-
ture) is a very good feature.
Several computer programs in BASIC are given in
an appendix and in worked-out examples in the text.
These can be used directly by the reader for simple
phase-equilibrium calculations.
The many homework problems are good, as are
the example problems worked out in the text. The
solutions manual seems to be complete and is a valu-
able companion to the book. The examples and prob-
lems in each chapter are related to real chemical en-
gineering situations, not just idealized problems as in
most texts. This distinction is especially important if
the book is to be used by practicing engineers.
Numerous phase diagrams and tabular data for
real systems are given, and a good (although quite
abbreviated) section on experimental techniques is
presented. Again, these are extremely important fea-
tures, as is the subject index, which can be used to
find these data quickly.
Although the book does contain several unique and
important sections, they tend to be too short. For
example, the section on experimental techniques is
only twelve pages long. Other weaknesses include a
complete lack of discussion about local-composition
mixing rules (or other mixing rules except the original
1890 van der Waals rules) or about continuous ther-
modynamics. In fact, not even a full page is devoted
to ill-defined mixtures, even though they are ex-
tremely important in the chemical processing indus-
tries. And although the chemical/physical model for
predicting fluid-phase equilibria for multicomponent
polar systems has been used extensively by industry
for several years, it is not mentioned. Perhaps the
most misleading part of the book is in the first chapter
where it is implied that the solution of a cubic equation
of state for its volumes is inherently iterative. In fact,
one of the advantages of a cubic equation of state in
industrial practice is that its roots can always be found
with a straightforward technique involving no itera-
Overall, Phase Equilibria in Chemical Engineer-
ing is a fine self-study and reference text for readers
who already understand the basic thermodynamics
which underlies the calculation of phase equilibria. It
proves a rapid introduction into the use of phase-
equilibrium models for chemical process design. The
many worked-out examples and the computer pro-
grams make it a worthwhile text for what seems to
be its targeted audience: practicing chemical en-
gineers who need to use thermodynamic models for
phase-equilibrium calculations immediately. E


j classroom



University of South Florida
Tampa, Florida 33620

tensively in chemical engineering to characterize
distributions of residence times in flow systems such
as reactors, packed beds, crystallizers and other pro-
cess equipment. The two extreme situations of plug
flow and complete backmixing are represented by the
uniform distribution and the exponential distribution
respectively [1]. Non-ideal flow situations between.
these extreme cases have been accounted for by popu-
lar models such as the dispersion model, the tanks in
series model and combinations of plug flow and back-
mixed models with dead zones.
Gamma distributions have been used in the litera-
ture for the characterization of distributions such as

the residence time distribution (RTD) and crystal size
distribution (CSD). This distribution can be used for
random variables with non-negative values. The
gamma distribution has been either derived from fun-
damentals, as in the case of the hopping model by
Rathor et al [2] for merging and splitting stream, or
used empirically for describing the distribution of a
random variable such as growth rate of the crystals
by Larson et al, [3]. This paper examines a physical
interpretation for a gamma residence time distribu-
tion through a statistical-mathematical analysis.
Consider N identical tanks in series with no inter-

Statistical Background Material
Probability density function fx(x) is defined such that if x is a ran-
dom variable, the probability that xe(x, x + dx) = fx(x)dx.
Expected value of xi is defined as

E(xJ) f xJfx(x)dx = Mx(j)


Note that the E[xt] = is also the jth moment of the probability
distribution about the origin, Mx(j).
For a non-negative random variable

ExJ] = x xf(x)dx = Mx(j)

(1 .2)

where Mx(j) = jth moment about the origin of fx(x)
Similarly, the expected value of a function g(x) can be defined as

E[g(x)] = f g(x)fX(x)dx

Kuttanchery A. Ramanarayanan (Ramu) received his Bachelor's
and Master's in chemical engineering from the University of Bombay
and his Doctorate from Iowa State University in 1982. Presently he is
an assistant professor in chemical engineering at the University of
South Florida. His research interests are in the areas of crystallization
from solution, chemical reaction-crystallization and mass transfer in
heterogeneous systems. (L)
William K. Howard received his BS and MS degrees in chemical
engineering from the University of South Florida. His research interests
are in the areas of heat exchanger fouling and he is a consultant for
heat exchanger design. (R)
Copyright ChE Division ASEE 1986



Consider the special case when
g(x) = exp(- sx)

E[exp(- sx)] = exp(- sx) fx(x)dx = (X(s)


>x(s) is the Laplace Transform of the probability density func-
tion, fx(x) and s is the Laplace variable for the random variable x.


mixing between the tanks. Let T represent the mean
residence time of the fluid element in each tank.
The total residence time of any fluid element in the
N tank system t is
t = t +t2 t3 + t4.. + t .. + (1)

where ti represents the residence time of the fluid
element in the ith tank. Since each tank is assumed to
be well mixed, ti is a random variable distributed ex-
ponentially having a distribution function [1]

fT(ti) = -exp I

Let s represent the Laplace variable for ti.
From Eq. (1)
exp(-st) = exp(-stI) exp(-st2)... exp(-stN)

Taking the expected values of both sides of Eq. (3)
with the assumption that ti's are random independent
E[exp(-st)] = E[exp(-stl)] E[exp(-st2)]...
...E[exp(-stN)] (4)

Since each tank is well-mixed and the residence time
distribution in the tank is represented by

fT(ti exp (5)

E[exp(-sti)] = exp(-sti) exp () dti (6)

T + (7

Non-ideal flow situations between these
extreme cases have been accounted for by popular
models such as the dispersion model, the tanks in
series model and combinations of plug flow and
back-mixed models with dead zones.

E[exp(-st)] = I( 1 N

(2) But from the definitions presented in Table 1, E[exp(-
s t)] is the Laplace transform of the function fT(t) with
respect to t, T(s) [4].
Taking the inverse Laplace transform of Eq. (8),

f (t) = tN-1 exp t
T TN r(N) (t

Comparing Eq. (9) with the standard equation for a
gamma distribution [5]

fx(X) 1 xa -1 expI
a r(o)

it is evident that a corresponds to the number of iden-
tical tanks and 3 corresponds to the residence time of
the fluid in each tank.
Table 1 lists some of the useful properties of the
gamma distribution. The product uc3 represents the
mean value of the random variable, in this case the
mean residence time of the fluid elements in the N
tank system. The variance of the distribution is ap2.

S 0.005

10 15

FIGURE 1. Typical plots of the gamma residence time
distribution for large values of a.

FIGURE 2. Typical plots of the gamma residence time
distribution for small values of a.


Properties of the
Gamma Residence Time Distribution

Form: f (t) = 1 t -1 xp- t
T a F(a) 8j

a > 0, 8 > 0

1) I fT(t) = 1

2) fT(t=0) = 0
3) Mean of the distribution, i = aB
4) Variance, a2 = a32
5) (CV)T = 1//r
6) The jth moment of f (t) about the origin:

M (j) = + j

7) *T(s) =- 1
(os + 1)a
where s is the Laplace Transform variable for t.

For the special case when a = 1, the gamma distribu-
tion reduces to an exponential distribution (one well-
mixed tank) and P3 corresponds to the mean residence
time in one tank T.
Figures 1 and 2 depict the shapes of the gamma
distribution for different combinations of a and p with
the same mean a3. It can be seen that for a large
value of a, the RTD is narrow and corresponds to the
plug flow situation illustrating that the plug flow sys-
tem is nothing but a combination of a large number of
small, well-mixed systems. Alternately, the gamma
distribution can be interpreted as the sum of inde-
pendent identical exponential distributions.


(CV)T coefficient of variation for the RTD
E[x] expected value of the random variable x
fx(x) probability density function for the random
variable x
g(x) moment generating function
Mx(j) jth moment about the origin of the probability
density function fx(x)
N number of identical tanks in series
s Laplace transform variable for t
t residence time of fluid element in the system
mean of the residence time distribution

Greek Letters
a parameter for the gamma residence time dis-
[3 parameter for the gamma residence time dis-
F(n) gamma function
F(a, P) gamma probability density function with
parameters a and P
+x(s) Laplace transform of the probability density
function fx(x) with respect to the random
variable x
T mean residence time

T residence time distribution


1. Levenspiel, 0., Chemical Reaction Engineering, John Wiley
and Sons, New York, 1972.
2. Rathor, M. N., L. G. Gibilaro and B. A. Buffham, "The Hop-
ping Model for Residence Time Distribution with Splitting and
Merging Streams," AIChEJ, ,1 (2), 327 (1985).
3. Larson, M. A., E. T. White, K. A. Ramanarayanan and K. A.
Berglund, "Growth Rate Dispersion in MSMPR Crystalliz-
ers," AIChEJ, 31 (1), 90 (1985).
4. Ramanarayanan, K. A., K. Athreya and M. A. Larson,
"Statistical-Mathematical Modeling of Continuous and Batch
Crystallizers," AIChE Symposium Series, 80 (240), 75 (1984).
5. Freund, J. E. and R. E. Walpole, Mathematical Statistics,
Prentice-Hall Inc., New Jersey, 1980. ]

REVIEW: ChE Thermodynamics
Continued from page 21.
count for thermal energy flow and work done by a
spontaneous process: for example, a power plant?
Thermodynamics is an exact mathematical struc-
ture based on exact differential forms. The relation-
ship between this structure and the independent vari-
ables used to identify the interactions of mass and
energy in physical systems and their surroundings re-
quires tight definitions, statements about the systems
and the interactions between the system and the sur-
roundings. Professor Daubert has not been very care-
ful with these details in this book.
The solved problems and exercises presented in
this book are certainly instructive. The ordering of
the material is unconventional but it will probably
work in the classroom. Take a careful look at the
theoretical development in this book. The application
of thermodynamics to a new problem is the test stu-
dents must pass after completing the thermodynamics
course. It is the careful development of these analyti-
cal skills that are missing in this book. El


Continued from page 11.
ments are conducted with the Department's hyperbaric chamber
Pieter Stroeve is studying the transport of respiratory gases in
blood and tissues, particularly the transport of carbon dioxide in
whole blood and tissues. Results from these studies will be impor-
tant in the design of artificial oxygenators and may provide a better
understanding of the relationship of pH and carbon dioxide partial
pressure in the body.
Robert Powell is conducting rheological studies related to sickle
cell anemia in order to understand the transition of a sickle cell from
a compliant to rigid behavior which can inhibit microcirculation. In
collaboration with the Department of Obstretrics and Gynecology,
he is also trying to elucidate the mechanical interactions between
spermatozoa and their environment through fluid mechanical and
rheological studies. The goal is to find a synthetic medium which
emulates cervical mucus and can therefore be used for clinical tests
and scientific research.
Alan Jackman is studying the arterial pressure regulatory
mechanism in the downstream arterial circulation of rats and dogs
to determine its role in the development of hypertension. Studies
in hypertensive rats have shown that the regulated pressure is
significantly higher in hypertensive rats than normal rats. This
work is carried out in collaboration with the Department of Human

Robert Powell's research in rheology focuses on experimental
and theoretical methods to characterize the mechanics of fiber sus-
pensions, such as those encountered in the processing of magnetic
coatings, advanced composite materials, and pulp fibers. For this
effort, a state-of-the-art rheological laboratory has been established
at U.C. Davis which includes instrumentation for routine testing
and facilities for highly specialized experiments, such as those in-
volving measurements on suspensions of conducting particles in an
electric field. In addition to investigating fiber suspensions, Powell
is investigating the effects of high-intensity ultrasound on physical
and chemical processes in fluids. An experimental investigation is
being carried out to confirm a theory recently developed by his
group which predicts that the addition of high molecular weight
polymer additives to water can drastically change nonlinear wave
Pieter Stroeve and Brian Higgins are interested in the problem
of drop breakup in shear flow. The dispersion of a liquid in an
immiscible liquid is an important process in industrial operations
such as extraction, emulsification, and blending. The present re-
search effort is concentrated on the drop breakup of polymeric sol-
utions in an immiscible polymeric liquid. This problem is important
in polymer mixing processes such as the dispersion of drops of color
concentrates or antistatic agents in a polymer solution.

Fluid Mechanics and Coating Phenomena

Small-scale multilayer flows are an integral part of several in-
dustrially important coating and extrusion processes. The impor-
tance of understanding the fluid mechanics of confined layered flows
is seen when precise control of the shape and location of the inter-
face separating adjacent layers is required. In small-scale flows
interfacial instabilities and interface distortion are usually un-
wanted complications that set limits on production rates and prod-
uct suitability, both of which impact the economics of the process.
Brian Higgin's research is directed toward understanding the fluid
mechanics and stability of layered flow of immiscible liquids in
which the effects of interfacial tension, contact line behavior and


fluid properties (density, viscosity) are important.
A key step in filament winding of composite structures is im-
pregnating the continuous reinforcement (bundle of untwisted car-
bon fibers) with a suitable matrix material such as an epoxy resin.
In this research Higgins is developing a fundamental understanding
of impregnation hydrodynamics. Analytical techniques and finite-
element methods are being used to study several prototype impre-
gnation flow geometries.
Single and two-phase flows in porous media are encountered in
many mass transfer and reactor design problems, in addition to oil
recovery operations and ground water flows. These flows are
strongly influenced by the heterogeneous nature of natural systems
in which it is necessary to predict both velocity fields and the trans-
port of solutes such as surfactants (in oil recovery) or pollutants (in
ground water flows). A theory of single phase flow in heterogeneous
porous media has recently been developed and a variety of impor-
tant extensions, notably two-phase flow and the dispersion of sol-
utes are being studied by Stephen Whitaker.

Process Dynamics and Control

Ahmet Palazoglu conducts research on the design and control
of chemical processes and plants in the presence of modeling uncer-
tainties. He is concentrating on the development of computer-aided
tools to guide the design process for large-scale plants. Control
system analysis and design studies are also being undertaken for
fixed-bed tubular reactors, to assess the impact of modeling deci-
sions and the selection of measured and manipulated variables on
the uncertainty handling capabilities of such systems.
Karen McDonald is investigating modifications of predictive
control algorithms which can compensate for process nonlinearity
in high purity distillation towers. A multivariable-gain-scheduling
technique and a variable transformation technique are used in these
studies. Both techniques are evaluated on complicated multicompo-
nent distillation problems as well as reactor control problems. A
long-range goal is the development of a general methodology to
determine pseudo-linearizing transformations for multivariable sys-

Thin Film Technology

The microelectronics and optical industries require the manufac-
ture of complex thin film structures with precise order, composition
and structure. Pieter Stroeve and Brian Higgins are investigating
different interfacial techniques for the manufacture of thin films.
The electrodeposition of metal alloys in microfeatures and the
Langmuir/Blodgett technique for constructing solid macromolecular
structures consisting of multilayers of molecules are being investi-
gated. This work is in collaboration with the Department of Electri-
cal and Computer Engineering.


Not all of the research has been described in the
previous sections. For example, there are collabora-
tive research projects with Los Alamos National Lab-
oratory and with Phillips Petroleum Company. Due to
space constraints, wisely imposed by this journal, we
now must give a short statement on the main points.
U.C. Davis is an active and growing department
which has built an excellent program in chemical en-
gineering. The students, the faculty, the staff, and
the department can be described as (according to one
of its members), "good looking and brains too." E


Sp O laboratory



Clarkson University
Potsdam, NY 13676

O UR UNDERGRADUATE FLUID mechanics labora-
tory consists of three experiments: mixing, drag
measurements, and fluid flow and pressure drop mea-
surements. The latter is the subject of this paper.
Like much undergraduate laboratory equipment, our
fluid flow apparatus was at least twenty years old. It
relied on a once-through gravity flow of local tap
water through iron and copper pipes which was not
only wasteful, because water was discharged directly
into the sewage system, but also introduced difficul-
ties in the winter due to dissolved gases in the water.
Instrumentation in the experiment included a venturi,
an orifice meter, a rotameter, a pitot-static tube and
two pipe lengths of copper and iron for measurements

Viroj Vilimpochapornkul received his BS in petroleum engineering
and his MSChE from Louisiana State University, and his PhD from
Clarkson in 1985. He is currently a Research Fellow at the Center for
Laser Diagnostics at Yale University. His research interests are heat
transfer and holographic interferometry. (L)
Nsima T. Obot received his BChE (1973) from Pratt Institute and his
MEng (1975) and PhD (1981) from McGill University. He has been an
assistant professor at Clarkson since 1980. His research interests are
in fluid mechanics and turbulence, and in heat and mass transfer,
with the current emphasis being on heat transfer in medicine and
biology. He has been involved with laboratory instruction since 1981
and is the laboratory director for the 1984-86 period. (R)

of friction factor. Data for pressure drop were ob-
tained using mercury and inverted air-water U-tube
Aside from being unnecessarily complicated, with
more than twenty valves (many of which had to be
manipulated simultaneously), the results obtained
with this old rig were often unreliable due to fouling
and corrosion. Also, since the cost for local water had
more than tripled during the past four years, it was
apparent that a straightforward solution would be to
replace the equipment. Prior to our decision to build
a rig ourselves, a careful evaluation of commercially
available laboratory teaching equipment was made.
Aside from the cost consideration of these units, at
least two separate rigs would be needed to accomplish
some of our objectives. Since acquisition of two or
more units would also involve laboratory space prob-
lems, purchasing the equipment became a less attrac-
tive alternative.
Several important criteria were established for the
new design. First, no more than a hundred gallons of
water should be used during one semester, a require-
ment that dictated the use of a closed flow loop. (This
value is less than one-half of the daily requirement for
the old experiment,) Second, piping material for the
test sections must be of clear plastic and pressure lines
must be of tygon plastic tubing, to enable visual obser-
vation of the flow pattern and purging of the system.
(Pressure lines in the old rig were of copper tubing.)
Third, the construction must be flexible enough so
that additional flow measuring devices and flow vis-
ualization techniques can be incorporated with
minimum effort and delay. (This was one of the under-
lying reasons for rejecting commercial units.) Fourth,
data for friction factor must cover the laminar, tran-
sitional and turbulent flow regimes.

The description of the experimental facility, shown
schematically in Fig. 1, is sufficiently detailed to per-
mit immediate incorporation into existing under-
graduate laboratory programs. It consists of an Ober-

Copyright ChE Division ASEE 1986


dorfer 13 HDL gear pump, driven by a 1.5 hp DC
variable speed motor, which delivers water from a
Nalgene 55 gallon polypropylene storage tank through
a back-flow preventing valve and into a Sears glass-
lined water tank (0.5m (OD) and 0.9m high). The lat-
ter, which is used as a surge tank, was salvaged from
scrapped equipment. The maximum pressure in the
surge tank is limited by a cut-off switch set at 30 psig
and connected to the motor controller power supply.
From the surge tank the water flows through three
transparent plastic pipes of internal diameter 50.8,
25.4 and 12.7 mm and then back to the supply tank.
The 50.80 mm diameter pipe loop contains a 12.7
mm diameter square-edged orifice (i.e. diameter ratio,
3 = 0.25) and also valved into this loop is an Ametek
6HCFB-61J laboratory rotameter (range: 1-24 gpm).
Upstream and downstream tap locations for the orifice
are one and one-half pipe diameter respectively. Aver-
age pressure at each location is determined from the
readings of three equally-spaced circumferential taps
using manifolds, the outlet from the manifolds being
connected to a U-tube mercury manometer. The flow
rate in the line is varied using the motor speed control-
ler. The reason for use of the latter rather than the
control valve is discussed later.
Flow through the three line segments of the 12.7
mm diameter loop, into which is also valved the smal-
ler range rotameter (4HCFB-40J, range: 0.1-5 gpm),
is controlled with a Whitey stainless steel valve hav-
ing a teflon seat and stem tip. Average wall static
pressures in two of these segments are measured by
flush-mounted pressure taps, spaced 0.61 m apart. In
each case, the upstream and downstream taps respec-
tively are 98 and 73 pipe diameters after and before
an elbow. At each location, the three circumferentially
placed taps, made from 1.6 mm (O.D.) brass telescop-
ing tubing, are connected to a manifold. The pressure



Several criteria were established for the design.
First, no more than a hundred gallons of water should
be used during one semester, a requirement that
dictated the use of a closed flow loop.

drop across the two 0.61 m lengths, to be used for
computation of friction factor, is recorded by a U-tube
manometer filled with a 1.75 specific gravity fluid and
by a Validyne DM 56 differential pressure transducer
assembly, the latter being designed to give direct digi-
tal readings in inches of water.
It is of some interest to note that after preliminary
tests in our laboratory, the original Validyne factory
sets were returned to the manufacturer for modifica-
tions. These included changing the transducer dia-
phragm, as well as recalibration of the unit, to give a
full-scale pressure range of 101.6 cm of water. Also,
the internal filter valve in the digital indicator was
changed to 0.1 Hz.
There are several additional comments. First, con-
nections at critical points (before and after each
rotameter, between the surge tank and the piping net-
work) are made with reinforced automotive radiator
hoses, as this facilitates modifications to the equip-
ment. Next, two purge valves are provided at the
inlets to each manometer. Also, since the principle of
operation of an orifice and a venturi is essentially the
same, the latter is not included in the new experiment.
Another general comment deals with the operation
of the equipment. Since each laboratory group con-
sists of three students, the recommended procedure
is to consider one flow loop at a time. When working
with the 12.7 mm diameter loop, the control valve in
one of the remaining loops must remain open for trans-
port of excess water back to the storage tank,
minimizing pressure build-up in the equipment.
As previously mentioned, flow through the orifice
is controlled with the motor speed controller rather
than with the control valve (Fig. 1). This decision was
made after the equipment was started several times
with the control valve completely closed. Apparently,
some students have had little exposure to flow control
with valves and are confused when it comes to decid-
ing which direction to turn a valve for open or close.
The consequences were exactly as might be expected:
damage to pressure lines and fittings, unwanted
shower baths, loss of mercury since no traps were
provided, and delay in completion of the experiments
because of time needed for repairs. For the 25.4 mm
and 50.8 mm diameter loops, the control valves should
be used primarily for isolation of a loop while variation
of the flow rate should be accomplished with the motor
speed controller. It should be noted that there is at


Orifice Discharge Coefficient

*Re x 10-: 0.17 0.36 0.52 0.59 0.64 0.81 0.92 1.07 1.13 1.22
Co : 0.64 0.65 0.64 0.64 0.62 0.63 0.63 0.64 0.62 0.63
*Based on orifice diameter

least one advantage to using the speed controller for
control; the scale (0 to 100) facilitates repeatability.


When the flow is initially started, bubbles in the
piping system are clearly visible and purging is easily
accomplished. Calibration of the rotameters and the
orifice, as well as pressure drop measurements, are
fairly straightforward and involve the collection and
weighing of water over an elapsed time. For low flow
rates (usually 0 to 60 mm reading on the smaller range
rotameter), the water collected is weighed on a Met-
tler 2000 electronic balance capable of reading as low
as 0.01 gm, while a Toledo scale is used for higher
flow rates. Since the pressure transducer must be
calibrated and no external source is provided for that
purpose, it is accomplished by using the actual pres-
sure drop in the pipe as measured by the 1.75 specific
gravity U-tube manometer for the turbulent flow re-
gime. The fact that the span (or gain) adjust control
on the digital transducer indicator can be set arbitrar-
ily permits use of different gain factors for different
laboratory groups. Since it is unusually difficult to ob-
tain accurate pressure drop readings with the U-tube
for low Reynolds numbers, construction of the com-
plete f vs. Re plot by any particular group depends on
the ability to establish the gain factor corresponding
to the setting on the control.
There is an interesting comment on the use of dif-
ferent gain factors. Here at Clarkson, each laboratory
group is required to submit a preliminary report prior
to performing an experiment and a final report upon
completion. Since these reports are produced using
our computer facilities, possible swapping of reports
and data was of some concern. Altering the gain of the
display was intended to reveal such a practice. Sur-
prisingly, although thirty-seven groups have used this
equipment, the fact that the gain was deliberately
changed from group to group has so far been unde-
tected by the students; at least no group drew our
attention to the differences in the gain of the display.

In addition to the plots of mass flow rate versus
rotameter reading and the square root of the pressure
drop for the orifice, each group is required to calculate

the orifice discharge coefficient (Co) for each Reynolds
number (Re). Typical results obtained by the students
are presented in Table 1 from which it can be readily
established that the average value could be stated as
0.634 0.010 for Re > 17,000 and P3 = 0.25, in close
agreement with the available literature [1] for an
orifice of comparable design.
For pressure drop, expressed in terms of the Fan-
ning friction factor, two plots are required: the famil-
iar log-log plot of f vs. Re and a linear plot of
1//Tvs. log1oRe/T
The first plot, typical results of which are presented
in Fig. 2, illustrates the transition from laminar to
turbulent flow, while the second (not shown here due
to space limitations), an alternative representation of
the same experimental data, is intended to familiarize
the student with the more practical concept of the
universal resistance formula for smooth tubes.
It can be seen in Fig. 2 that the students' results
for turbulent friction factor are closely approximated
by the well-known Blasius equation. Although the
laminar results are not as accurate as one would wish,
due primarily to the resolution (0.01 inch of water) of
the digital transducer indicator, they nonetheless con-
firm that transition from laminar to turbulent flow
occurs in the range of Reynolds number between 2,000
and 3,000. For laboratory instruction, the resolution
of the digital indicator is quite satisfactory.

Up to this point, we have dealt with the general
features of the equipment, experimental procedures,
and some of the results. In this section, we will briefly
describe two features that have been included in the
experiment. The first, a reflection of the latest
technology in flow measurement, involves installation





of an Eastech 2350 vortex shedding flowmeter. This
unit is valved into a separate, clear plastic, pipe loop
as shown in Fig. 1. Internal diameter of the pipe is
25.4 mm, this loop's control valve being also of stain-
less steel. With the ancillary signal processor, digital
display of the flow rate (in gpm) is obtained. Since the
fluid flowing past this device is fed to the rotameter
(Fig. 1), this meter's readings can be compared with
those obtained by weighing. Also, the straight en-
trance length required before the meter and the fact
that the minimum measurable flow rate is much
higher with a 50.8 mm than with a 25.4 mm diameter
pipe, necessitated inclusion of a separate pipe loop.
The choice of a vortex shedding flowmeter over
other sophisticated and nearly fool-proof systems, was
made because of its educational value. In the first
place, its principle of operation (that of vortex shed-
ding when real fluids flow past submerged bluff ob-
jects) is a natural phenomenon and is usually covered
in undergraduate fluid mechanics course. Also, with
clear plastic pipe, the vortex shedding frequency can
be observed using a strobe-light assembly.
Another feature that has been incorporated in-
volves installation of a series of 1.6 mm diameter
flush-mounted pressure taps upstream and down-
stream of the orifice. This is intended to highlight the
dependence of orifice discharge coefficient on pressure
tap locations, as well as the trends in pressure distri-
bution in the vicinity of surface mounted protrusions.

The design of a versatile fluid flow experiment for
undergraduate instruction has been presented. The
flexibility in design and construction facilitates addi-
tion of some of the latest technology in flow measure-
ment. The equipment is inexpensive when compared
to the cost of commercial units with limited features.
In addition to the supplies, about a week of a techni-
cian's time is required for construction of the unit.
As to the laboratory teaching procedure, it may be
noted that each group of three is required to carry out
this experiment, and drag measurement or mixing,
during a two-week period. Even with the additional
features noted above, seven hours of laboratory time
are allowed for this experiment, as is the case for the
other fluid mechanics experiment. Groups that do not
complete an experiment during the scheduled period
are required to do so on their own time. In general,
each group is required to give an oral progress report
after completion of the first of two laboratory periods.
Plots of all data obtained during the first laboratory
period, along with typical calculations, must be pre-
sented to the instructor just before the oral presenta-

1. Chemical Engineers' Handbook, R. H. Perry, et al. (eds.),
5th ed., McGraw-Hill, N.Y. 1973. D

book reviews

By Frank P. Rinehart
Wiley Educational Software, Wiley & Sons, Inc.,
$25.00 (1984)
Reviewed by
Pradeep B. Deshpande and Walden L. S. Laukhuf
University of Louisville
The Chemistry Tutor consists of programs de-
signed for use with the APPLE II+ or IIe computer
with a disc drive and DOS 3.3. The programs deal
with balancing equations, stoichiometry, and limiting
The first set of programs is designed to teach the
user how to balance chemical equations. The exercises
ask the user to select the coefficients in the equation,
and the program checks whether the equation is bal-
anced. If the equation is balanced the user moves on
to the next exercise. If not, another set of coefficients

may be entered and checked for correctness. The user
has the option to ask for help through a tutorial. The
tutorial asks how many atoms of each element are
present on each side of the equation. Sooner or later
the reader discovers what element is not in balance.
The second segment deals with stoichiometry. The
exercises enable the user to decide how much of a
reactant or product is consumed or formed given the
mass of any other reactant and product. The final set
of programs is concerned with limiting reagents. The
objective, in this instance, is to decide how much of
any product could form given the specified amounts of
two reactants, when one of them is a limiting reagent.
The programs are well written and are user
friendly. Unfortunately, the exercises are too elemen-
tary for college level students. The usefulness of the
programs would be enhanced if the author could be
persuaded to include the analysis of redox reactions
by change in oxidation state or ion-electron technique.
The reviewer was assisted by Prof. Emeritus P.
M. Christopher in the review. His assistance and com-
ments are gratefully acknowledged. L-


design 1


Stevens Institute of Technology
Hoboken, NJ 07030

tory was initiated as a senior course at Stevens
Institute of Technology in 1968. It is a six-credit
course and follows our course in process design. Both
courses are related, giving the student a complete ex-
perience in chemical engineering design. In 1973 the
philosophy and organization of the laboratory was de-
scribed [1]. Since that time we have been developing
a systematic approach to designing the systems and
operating the laboratory which are described in this
The design laboratory is an example of an expe-
riential learning activity. In 1976 Harrisberger et al,
[2] described the experiential learning process and
evaluated several current programs. They grouped
experiential learning activities into two classes: simu-
lations and authentic involvement. "Simulations con-
sist of contrived situations that are carefully designed
to meet selected learning objectives and are under

Harry Silla is professor of chemical engineering at Stevens Institute
of Technology. He obtained his BS degree from City University of New
York and his MS and PhD ('70) degrees from Stevens. Before complet-
ing his PhD he was a project leader at AeroChem Research Laboratories
in Princeton, NJ. He is the coordinator for courses in chemical engineer-
ing design at Stevens. He has also served as a member of the New
Jersey Solid Waste Task Force, advising on solid waste processing. His
current research interests are in coal liquefaction kinetics and process

close faculty control. The Authentic Involvement ac-
tivities expose the student to real situations with to-
tally open-ended outcomes, although the faculty may
influence the selection of the situations and set perfor-
mance criteria to assure that positive learning objec-
tives are met." Harrisberger et al further state that
besides being open-ended the authentic involvement
models involve ". . unstructured activities, origina-
ting off campus . ." For simulations they identified
the following models: the experimental laboratory,
guided design, case studies, and games. For authentic
involvement models they identified: internships, con-
sulting, and clinics or design centers. According to
Harrisberger et al all authentic involvement uses out-
side clients, which may be industrial firms, gov-
ernmental agencies, civic organizations, institutions,
or private individuals. It should not be necessary that
an outside client generate projects. The essential fea-
ture of an authentic involvement activity is that it
should be open-ended. Although most projects in the
design laboratory have been originated on-campus by
our faculty, the projects are open-ended and the oper-
ation of the laboratory is unstructured. Thus we be-
lieve that the design laboratory is an authentic in-
volvement activity. Projects generated by the faculty
have the advantage of promoting a greater involve-
ment of the faculty in the course.

Several modifications in the content of the labora-
tory have been made since it began, but the main ob-
jective has always been to use the laboratory ". .. as
a vehicle for teaching design. . ." [1]. Also, ". .. an
important objective of the design laboratory is that
the student develop the skills required to reduce his
design calculations to practice. . ." [1]. As it has
been pointed out, training in design is not only useful
for those who undertake a career in design, but also
for those who enter research and development and
who will frequently be required to design their own
experimental systems [1]. Early in the development
of the course the collection and analysis of data was
considered an additional objective of the course, but
later it was decided that this is not a design objective.
Copyright ChE Division, ASEE, 1986


Presently, the only data required is that which is
necessary to demonstrate that the system operates as
designed. Producing a working system is the main
consideration. At the beginning it was recognized
that, in addition to the design experience, the student
obtained a complete experience, starting with project
conception and ending with its implementation. Later,
it was found that training to plan, execute, and com-
plete an engineering task, specifically project manage-
ment, was also necessary [3]. This particular aspect
of the course, which is still being developed, is gener-
ally useful whether the engineering task be process
development, process design, or project engineering.

The essential feature of an authentic involvement
project is that it be open-ended, although Harris-
berger et al stated that the project should originate
off-campus, probably because in the course models
they considered the projects were originated by off-
campus clients. At Stevens most of the projects origi-
nate on-campus. Although the work may be done on-
or off-campus, or in some combination, we prefer that
the work be done on-campus so we can maintain better
control over the projects and also so we can continu-
ously observe and improve the learning process and
environment. Sources of projects and examples of pro-
jects were given earlier [1]. More recent examples of
projects are listed in Table 1. Several projects have
been to design and construct experiments for other
chemical engineering laboratories and for faculty re-
search projects. In these cases a faculty member be-
comes the client. Several systems have been designed
and built by the students over the years. The projects
may involve the design of new systems or new subsys-
tems for existing systems. Recently, completed pro-

Selected Design Laboratory Projects
1. Design of an automatic carbon dioxide makeup system for
a gas absorber recycle stream.
2. Design of an adsorber for removing phenol from waste
3. Design of a fermenter for producing cellulase enzyme.
4. Design of a distillation column using York-Twist packing.
5. Design of a sonochemical reactor for producing
6. Design of an equilibrium flow cell for measuring the solu-
bility of carbon dioxide in crude oil.
7. Design of an electrochemical reactor for reducing ketones.
8. Design of a packed bed catalytic reactor for producing
methane from carbon dioxide and hydrogen.
9. Design of an artificial kidney with continuous removal of
urea from dialyzate.
10. Design of a membrane process for stripping monomer from
latex solutions.

. training in design is not only useful
for those who undertake a career in design, but
also for those who enter research and development
who will frequently be required to design
their own experimental systems.

FIGURE 1. Phases of a design project.

jects have been expanded by designing control sys-
tems. An example of a subsystem was the addition of
a carbon dioxide makeup system to an absorber. This
required designing a sampling system to analyze the
carbon dioxide in the exit gases from the absorber and
a system for automatically feeding of makeup carbon

The general structure of any project is shown in
Figure 1. A team of three students selects a project
from a list. We have experimented with team sizes of
one to four and have found that three is optimum.
Working alone is generally not beneficial for the stu-
dent, and a team of four tends to be inefficient. Stu-
dents prefer working with a group so they can readily
discuss their project and test their ideas. After the
project is selected, the project definition phase begins
which first requires familiarization with the project.


At the beginning, references are usually provided.
Additional information can be obtained from the liter-
ature, the faculty in general, industry, or any other
source. As the student becomes familiar with the pro-
ject he generates block flow diagrams to illustrate al-
ternative designs, and he eventually writes a prelimi-
nary proposal to outline the scope of the project for
the semester. Further refinement of the project goals
is achieved by conducting an informal project review
with at least two faculty members.
After the project has been defined, the design
phase begins with the construction of a process flow
diagram. The type of diagram we have found to be

From his evaluations and tests he found
that that particular thermometer was the most
reliable. It was the experience of his company that
equipment which looks the best is
often the most reliable.

most useful is one that contains all the major equip-
ment, valves, and instrumentation. Following this,
mass and energy balances are made, and all the equip-
ment appearing on the diagram are sized. Because
flow system design appears in nearly all projects, the
topic is taught in our process design course which pre-
cedes the design laboratory. Simultaneously, most
equipment is selected from catalogs, evaluated, and
ordered. If some equipment is not available commer-
cially, it must be designed and fabricated. Because of
the time required to fabricate special equipment, we
make a considerable effort to find an alternative
method which uses standard equipment. While wait-
ing for the delivery of the major pieces of equipment,
the piping system is designed by first laying out the
equipment and then constructing an isometric draw-
ing. At the same time, equipment and piping supports
are also selected.
Accurate drawings are needed to reduce construc-
tion errors and to produce a reliable, aesthetically
pleasing system. There appears to be a relationship
between aesthetics and reliability, as pointed out by
Hathaway [4]. At the beginning of his talk, Hathaway
passed out several dial thermometers and asked the
audience to select the best one. At the end of the talk
he tallied the votes, and it was found that the ther-
mometer which looked the best obtained the most
votes. From his evaluations and tests he found that
that particular thermometer was the most reliable. It
was the experience of his company that equipment
which looks the best is often the most reliable. Obtain-
ing an acceptable drawing from students is rare. On
a trial basis we have attempted using a draftsman,
but this was only partially successful because of the

cost and the number of drawings required in a short
time. The next step will be to develop a computer-
aided drafting program suitable for the course.
Finally, the implementation phase of the project is
reached. It consists of construction, testing, trouble-
shooting, and the final adjustments necessary to pro-
duce a working system. This phase provides the
necessary feedback for the student to gain confidence
in his design procedures.

In addition to process design, a successful project
also requires careful consideration of the mechanical
aspects of the design, including fabrication
techniques. Surprisingly, it is difficult to instill the
importance of insuring that the various parts of an
apparatus fit, are properly sealed and are securely
supported. Instruction in these techniques must be
provided in the course. Some of the required
techniques are unique to a project while others are
more general, such as piping. Since we keep the size
of the systems as small as possible (to minimize the
cost, the space required, and the time to assemble the
system), small diameter tubing is adequate for the
piping. For a number of years a local company has
lectured, instructed, and demonstrated on the selec-
tion of fittings and valves and the assembling of flow
systems with tubing. Since the introduction of these
topics into the course, the reliability and aesthetics of
the systems have improved considerably. Seal design,
another generally useful topic needed for designing
safe and reliable systems, will also be treated more
systematically than it has.

Students, as well as professors, are hopeful that
given enough time they will be able to do a better job.
At the beginning not much consideration was given to
the student's need to develop techniques of planning
his operations to fit within a fixed time frame. Pro-
crastination is always a problem, but most students
have a strong desire to complete their projects and to
do well. The design laboratory project is more com-
plex than other activities which they have encoun-
tered up to this point in their careers. Also, they must
coordinate their activities with other members of their
team. Because students are inexperienced in planning
and organizing their activities jointly, we have gradu-
ally developed project management techniques for the
course. In this activity students are instructed to
break up their project into tasks and to schedule their
project for completion in fourteen weeks by computer
using the critical path method. The Gantt chart is also


utilized. Responsibility for each of the tasks is then
assigned to each member of a three-man team.
Further control over a project is established by
requiring each team to submit weekly progress re-
ports where progress during the past week is de-
scribed, problems are discussed, and plans for the fol-
lowing week are outlined. In addition to the weekly
reports, extensive monthly reports and a final report
are required. The monthly reports are cumulative,
which means that the second monthly report uses the
first monthly report as a base, making the necessary
corrections, improvements and additions. The final re-
port uses the second monthly report as a starting
point. This procedure for writing reports is a very
effective way of obtaining an acceptable final report.

The students are responsible for the execution of
their project, and they are urged to seek help when
needed. Except for the initial project review there
are no other scheduled reviews. The coordinator is a
consultant who suggests courses of action and sources
of information, both internal and external. Occasion-
ally, if it is perceived that a project is stagnating or
that the project direction is not clear, as indicated by
the weekly reports, the project team will be required
to report orally to the course coordinator.
Teaching assistants are assigned to the course and
are useful during the design phase of the project.
Later, when equipment must be selected and
evaluated, and during the mechanical design phase,
teaching assistants are less effective. Teaching assis-
tants are also used to control the flow of tools, to reg-
ulate the ordering of equipment and supplies, and to
maintain laboratory safety and construction stand-
To make the laboratory function, a variety of
mechanical skills is needed. It is unrealistic to expect
that students will have all these skills, but they should
understand the principles and limitations of each
technique used in their project. Our goal is to limit the
student's laboratory activity to assembling their sys-
tem from components and to testing the completed
system. Because of the large demands on our machine
shop, we use our shop for only small jobs and utilize
outside sources for major machining, welding, glass
blowing, and other specialized skills. The students
coordinate these activities, making all the arrange-
ments, providing drawings, and filing requisitions for
the work.
We do not rely entirely on a storeroom of equip-
ment for projects. Ordering most of their equipment
is considered part of the student's experience in the

course. Various companies have donated equipment
to the laboratory, helping to reduce the cost of opera-
tion. Funding for the laboratory has been provided by
Institute funds and by general funds given to the de-
partment by industry. Occasionally, grants have been
given directly to the laboratory. Last year we had a
total of seven projects costing about $2000 per project.
On the final day of the course each team is required
to demonstrate the workability of their project during
an open house. This is an exciting day, and the results
have been gratifying. Grading is determined by the
degree of completion of each project, performance
during the semester, and the quality of the reports.
There is no doubt about the value of the design
laboratory in developing the ability and confidence of
the students to translate their calculations into a
working system and in giving them the satisfaction of
obtaining a finished product. The design laboratory
compliments our course in process design, giving the
student a complete design experience. During the
semester one can see considerable improvement in the
ability of the student to apply his knowledge to a real
situation, to make technical decisions, to overcome ob-
stacles, and to manage a project. It is believed that
the design laboratory experience shortens the time
period required for a student to become a productive
employee after he enters industry.
We are grateful to Chevron U.S.A., the Exxon
Research and Engineering Co., The Filtration Society
(New Jersey Section) and the Otto H. York Co. for
funding or donating equipment to the design labora-
tory. We are also grateful to Mark Dinnerman of Com-
ponents and Controls (New Jersey) for providing in-
struction on the mechanical aspects of constructing
flow systems with tubing, to Richard Palluzzi of
Exxon Research and Engineering for lecturing on
pilot plant safety, and to Cheryl Teich of the Rohm
and Haas Co. for suggesting that we have a projects
demonstration day at the end of the semester.
1. Silla, H., "The CHE Design Laboratory," Chem. Eng. Ed.,
11, 1,129, 1973.
2. Harrisberger, L., R. Heydinger, J. Seeley, M. Talburtt,
"Experiential Learning in Engineering Education," ASEE,
Washington, DC, 1976.
3. Silla, H., "The Chemical Engineering Design Laboratory,
Compendium on Engineering Laboratory Instruction,"
ASEE, Washington, DC, 1982.
4. Hathaway, R., "Selection and Application of Process Instru-
ments," Seventeenth Annual Symposium, New Jersey-North
Jersey Sections of the AICHE, 1977. []


class and home problems

The object of this column is to enhance our readers' collection of interesting and novel problems in
chemical engineering. Problems of the type then can be used to motivate the student by presenting a
particular principle in class or in a new light or that can be assigned as a novel home problem are re-
quested as well as those that are more traditional in nature that elucidate difficult concepts. Please sub-
mit them to Professor H. Scot Fogler, ChE Department, University of Michigan, Ann Arbor, MI 48109.


The University of Akron
Akron, OH 44325

The Seta Point Detector is an instrument used for
studying the cold flow properties of jet fuel. The part
of that instrument of interest here is the chamber wall
and the fuel next to it (see Figure 1). Fuel is cooled
as it rises and falls along the vertical cooling walls of
the chamber. In normal instrument usage cold fuel
becomes highly viscous, often due to the formation of
wax particles. Part of the view through a transparent
piece (viewport in Figure 1) into the fuel chamber
lines up in such a way as to provide a wax profile
should it form on the chamber wall. A flowing wax
film formed while this writer was engaged in another
study [1] involving, in part, photography through the
transparent port. The recorded flow situation is
shown in Figure 2. Notice that the film initially
showed a classical parabolic profile, but then de-

Dale L. Schruben received a BS in physics and a BS in nuclear
engineering from Kansas State University, a MS in chemical engineer-
ing from the University of Minnesota and his PhD in chemical engineer-
ing from Carnegie-Mellon University. He has industrial experience
with Westinghouse and Exxon, and his research interests are in pe-
troleum rheology and transport problems.



uel/wax film flowing on the fuel cha

veloped a curious ripple that traveled to the bottom
of the chamber. (A reader not interested in the details
of the modeling process may skip the remainder of
this background statement and simply assume the
problem to be modeled by an unsteady, nonisothermal
Shortly after the formation of the wax film, cooling
MMOORE ceased, although the cyclic fuel flow continued. While
fuel was at maximum height along the wall some wax
was probably added to the film, although the photo-
graphs suggest this was minimal. Density of film and
fuel were probably close enough so that at maximum
fuel height the film was supported buoyantly by the
fuel, and thus the film had no tendency to flow. How-
ever, at minimum fuel height, unopposed gravitational
body forces did cause the free standing film to flow in
V-n% a slump toward the bottom of the chamber. Residual
temperature gradient must have remained across the
Copyright ChE Division, ASEE, 1986








FIGURE 2. Profile of falling wax film, where 8 is film
thickness, Z is vertical distance down the wall, and the
tl, t2, t3 are successive times.

film even though wall temperature change was mini-
mal since its cooling had ceased. The above considera-
tions suggested the film be modeled as a classical film
that flows over time equal to the sum of the free stand-
ing periods [1].
Two paths could lead students to this point in the
development of the problem. They could be given the
full experimental description and asked to construct a
model and analyze it. Alternatively, they could be
given the statement that a classical parabolic film
exists, only nonisothermally and unsteadily with vis-
cosity increasing linearly from the outer edge of the
film due to the temperature gradient, and asked to
show that this model qualitatively describes the film
and the ripple. It should be added that the inner wall
constant temperature is colder than the constant tem-
perature of the outer free film surface. Of course, the
flow profile would not be parabolic with variable vis-
cosity. This and other considerations such as surface
tension are under study, but early indications are that
this simple model is worthwhile given the information
it provides.
Origin of the ripple in Figure 2 may be explained
from consideration of a packet of the film small enough
to be isothermal. The film packet wants to fall down-
ward due to gravitational body force. Since viscosity
increases as distance from the outer edge of the film,
the packet necessarily falls into a region of higher vis-
cosity. In simplistic terms, it wants to go somewhere
so it bulges out to form the hump of the ripple. It does
this at intermediate z values (lengths down the wall),

perhaps because at large z values the film becomes
isothermal relative to a differential mass balance,
while at small z values the thermal gradient and high
viscosity retard flow development.
Let that intermediate z region be defined as that
in which the basic flow profile is parabolic, but the
viscosity depends on horizontal position from the
outer edge of the film. The unsteady state mass bal-
ance (with mass profile 8) yields

36 a J py62[/6) (1 2)(6)2]dy
at 2z no[l + K1(6-y)]

Eq. (1) reduces to the classical form [1] when K, = 0.
At this point the clue is given that K, is small so that
1 + K6-) ~ 1 K,(6-y) (2)

This is identical to the first order approximation of
the well-documented exponential law, 'q = 9qo exp(-Ki
(T To)), with temperatures T, To proportional to dis-
tances y, 8.
The integration is now simply performed to yield

56 + 62 -6 K2 3 D6 a 0
at a-X a x

if x = zqo/pg and K2 = K1/2. A perturbation expansion
solution in terms of the small parameter K2 is assumed

6 0 + K261

where the second order solution satisfies

tat 1 + x t

The second clue is now given that they try for 81 a
power series in the known first order solution 80 =
Vx/t. From this they find the particular integral
61 = 1/2 (x/t) (6)

which completes the perturbation solutions (see Fig-
ure 3).
The Eq. (4) solution has a ripple, but it falls faster
than the experiment-not surprisingly, considering
the simplistic assumptions.
If the similarity transformation v = x/t, 8 = f(v),
is made on Eq. (3), it becomes
6f (f2 2 Kf3) = 0 (7)

Since in general the derivative is not zero, the cubic
expression must be. The negative values of f (reflected
to be positive) approach the experiment closer than
Eq. (4), but they do not have a ripple, except in the





t=1 l

4 ,f

FIGURE 3. The perturbation solution, 8, (a) in compari-
son to the classical, bo, (b) and cubic, f, (b) solutions (K2
= 0.5 and t = 1 unless otherwise indicated).

limited sense that the profile is thicker and higher on
the wall relative to the classical profile (see Figure 3).
The perturbation and analysis do interestingly
exercise development of insight, are qualitatively re-
warding, and introduce perturbation ideas with a
minimum of mathematical complexity. Eq. (7) pro-
duces a more realistic shape (without ripple), but a
better model is needed with realistic general shape as
well as details (ripple).

Acknowledgements are due to an ASEE Summer
Faculty Fellowship, The University of Akron Re-
search Grant (RG-804), NASA grant NAG3-488, and
to the memory of Bert Phillips and his interest in this
t = time
8 = film thickness
y = horizontal distance from wall into the film
z = distance down the film
x = dimensionally modified distance
= z' o/pg
p = density
g = acceleration of gravity
q = viscosity for film interior
o = viscosity at the outer edge of the film
KI = proportionality of viscosity to distance from
outer edge of the film
K2 = K1/2

1. NASA-ASEE Lewis Summer Faculty Fellowship Program
1984 Final Report, Case Western Reserve University, Uni-
versity Circle, Cleveland, Ohio 44106.
2. R. Bird, W. Stewart, E. Lightfoot, Transport Phenomena,
Wiley, Problem 2. R. []

LN 0 book reviews

by James W. Cooper
John Wiley & Sons, Somerset, NJ 08873,
1984, $29.00
Reviewed by
Richard Heist
University of Rochester
The subtitle of this book is Programming in Pas-
cal and MC68000 Assembly Language on the IBM
System 9000. The first two chapters provide the "in-
troduction" to the System 9000. By "introduction," I
mean a discussion of the operating system, file handl-
ing and the system editor! Chapters eleven and twelve
are actually part of the introduction as well, since a
partial review of the system library functions and a
brief discussion of the display screen and console box
are presented. Chapters three through ten provide an
introduction to Pascal. The second half of the book
deals with assembly language programming on the
MC68000, the microprocessor used in the System
9000. Nine chapters are devoted to assembly language
programming with one of those nine describing how
to use the assembler on the System 9000. The last
chapter in the book provides several Pascal and as-
sembly language programs for drawing diagonal lines
on the graphics display and one for reading in and
displaying a 16K plot.
In the Preface the author states that "This book
gives the scientist a basic introduction to Pascal,
shows how to program this computer system, and
gives a brief introduction to the assembly language of
the Motorola 68000. . ." I agree with two of the three
statements. It is a basic introduction to Pascal and it
is certainly a brief introduction to assembly language
programming on the MC68000, but I seriously doubt
that a scientist could effectively ". . program this
computer system" with the information provided in
this book. Having seen the documentation IBM pro-
vides for the 9000 and having seen firsthand the diffi-
culty several of our better students have had learning
to program the System 9000 over the course of an
entire semester, I have some appreciation for the ef-
fort involved in using the System 9000 in a laboratory


The chapters devoted to Pascal are probably
adequate to become acquainted with the language pro-
vided one has had prior programming experience. I
would not recommend this text to a novice. The author
provides a number of examples in the form of sample
programs which are useful; but, in my opinion, it
would be much better if he also provided exercises.
The MC68000 is a powerful microprocessor, but it
is relatively complicated (compared to, say, the 6502)
to program and use effectively as a laboratory instru-
ment. In my opinion the brief introduction to MC68000
assembly language programming in chapters 14 to 21
is inadequate, even for someone who has had experi-
ence. The addressing modes are one of the most im-
portant and powerful features provided with the
MC68000 instruction set. Yet to spend only one short
chapter discussing the addressing modes and to pro-
vide virtually no practice exercises is extraordinary.
Assembly language programming for 16 (and larger)
bit processors gets to be cumbersome without the use
of an assembler. ASM, the assembler provided with
the System 9000, is a crucial part of the system and
also deserves more than one chapter if it is to be
learned effectively. Again, practice exercises would
be very helpful.
Although the author does not suggest it specifi-
cally, it seems that this book might better be de-
scribed as an adjunct to the documentation provided
with the System 9000. The eclectic approach used in
the book should help to keep the many details in the
system documention in perspective and, at the same
time, provide an easier path toward getting the Sys-
tem 9000 doing something useful. OE

Continued from page 7.

calculations for multicomponent aqueous systems containing vol-
atile, weak electrolytes and other gases. To solve the equations of
phase equilibrium, we use the method of Nakamura et al [3] to
calculate fugacity coefficients in the vapor phase; for the liquid
phase, we use Henry's constants and an extension of the theory for
electrolyte solutions developed by Pitzer [4] to describe the tem-
perature and concentration dependence of activity coefficients. A
sophisticated numerical technique is used to solve the many simul-
taneous equations of equilibrium.
3. Gas-Hydrate Phase Equilibria presents a program for calculat-
ing the conditions of pressure, temperature and gas composition
required for formation of hydrates. Gas hydrates are formed when
water and light gases (e.g., natural gases, refrigerants, oxygen,
nitrogen) are at equilibrium at low temperatures and high pres-
sures. Gas molecules become trapped in cavities (or cages) con-
tained in the crystalline lattice structure formed by water
molecules; the trapped gas molecule stabilizes the lattice. A quan-
titative understanding of conditions for hydrate formation is neces-
sary, for example, to design gas production from underground fields
of natural-gas hydrates, or to control sea-water desalination plants

where hydrates are used to separate water from salt. Hydrate-for-
mation is particularly important in the transportation of natural
gas, where hydrates can clog pipelines. In this case study, we use
a modified van der Waals-Platteeuw [5] framework to estimate hyd-
rate-formation conditions. Fugacities in the vapor phase are com-
puted from the Chueh-Prausnitz [6] modification of the Redlich-
Kwong equation of state.

4. Isothermal Flash Calculations for Multicomponent Mixtures of
Organic Liquids Using UNIFAC combines the UNIFAC method
[7] for establishing activity coefficients with a step-limited Newton-
Raphson routine to assist the user in performing isothermal flash
calculations for a wide variety of mixtures of organic liquids, con-
taining up to 10 components. We use an isothermal flash calculation
to obtain the pressure (or temperature) that produces the optimum
separation of two hydrocarbons from a multicomponent stream. The
program includes a data bank with group surface areas, group vol-
umes and group-group interaction parameters as required to calcu-
late activity coefficients with UNIFAC.

5. Estimation of Activities of Solvents in Polymer Solutions Using
UNIFAP, uses an extension of the UNIFAC method for calculation
of liquid-phase activities of solvents in polymer solutions. In
polymer production, these activities are required to design de-
volatilization equipment, necessary to recover the solvent from the
polymer solution by evaporation. UNIFAP [8] is a group-contribu-
tion method that can be used to estimate vapor-liquid equilibria for
a variety of polymer mixtures where no experimental mixture data
are available. The computer program includes a data bank which
contains the pertinent group parameters.
Copies of these case studies are available from J. M. Prausnitz
(Department of Chemical Engineering, University of California,
Berkeley, California 94720). Magnetic tapes for computer programs
(written in FORTRAN IV) are available for purchase. These tapes
are 9 track at 1600 bpi, in EBCD with 80-character (card-image)
The undersigned are grateful to the Camille and Henry Dreyfus
Foundation, New York, for financial support and to V. Brandani,
E. M. Pawlikowski and F. E. Anderson for extensive assistance in
preparing the case studies. They welcome comments on the use of
these case studies for education of future chemical engineers.
J. M. Prausnitz
E. G. Azevedo
University of California, Berkeley

(1) Lowenheim, F. A., and M. K. Moran, Faith, Keyes, and
Clark's Industrial Chemicals, 4th Ed., John Wiley, New York
(2) Hayden, J. G., and J. P. O'Connell, Ind. Eng. Chem. Proc.
Des. Dev., 14, 209 (1975). See Reference (9).
(3) Nakamura, R., G. J. F. Breedveld, and J. M. Prausnitz, Ind.
Eng. Chem. Proc. Des. Dev., 15, 557 (1976).
(4) Pitzer, K. S., J. Phys. Chem. 77, 268 (1973).
(5) Van der Waals, J. H., and J. C. Platteeuw, Adv. Chem. Phys.,
2, 1 (1959).
(6) Chueh, P. L., and J. M. Prausnitz, Ind. Eng. Chem. Fund.,
6, 492 (1967).
(7) Gmehling, J., P. Rasmussen, and A. Fredenslund, Ind. Eng.
Chem. Proc. Des. Dev., 21, 118 (1982).
(8) Oishi, T., and J. M. Prausnitz, Ind. Eng. Chem. Proc. Des.
Dev., 17, 333 (1978).
(9) Prausnitz, J. M., E. A. Grens, T. F. Anderson C. A. Eckert,
R. Hsieh, and J. P. O'Connell, Computer Calculations for
Multicomponent Vapor-Liquid and Liquid-Liquid Equilibria,
Prentice-Hall (1980).


Continued from page 17.
In many applications it is important to know which
branch of steady state solutions is reached following
an ignition or extinction due to a slow variation of an
operating or control variable. This information may
be extracted from bifurcation diagrams (for example,
Fig. 2). To find the various types of possible bifurca-
tion diagrams we write the steady-state equation as

F(y,i,p) = 0 (28)

where ji is the bifurcation variable and p is a vector
of parameters which are independent of J.
The singularity theory with a distinguished
parameter, developed by Golubitsky and Schaeffer
[23, 24], enables a systematic prediction of the various
types of local bifurcation diagrams that Eq. (28) has.
The theory is based on the fact that regions of
parameters with qualitatively similar bifurcation dia-
grams are separated by hypersurfaces which coalesce
at highly degenerate (singular) points. These singular
points are characterized by certain qualities and in-
equalities involving the partial derivatives of F with
respect to y and pL. The theory enables one to replace
the analysis of the complex function F by that of a
simpler function (usually a polynomial) g(w,X) = 0,
called the normal form. For example, any function
F(y,[ ) which satisfies at (0,0) the qualities

F=F =F =F =F =0
y 11 yY YP

and the inequalities
F > 0; F > 0 (30) X

is qualitatively similar (contact equivalent) to the
winged cusp singularity g=w3 + X2=0.
A systematic procedure for finding the normal
form was developed by Golubitsky and Schaeffer [23,
24]. Moreover, there exist published tables classifying
the qualities and inequalities for various normal
forms [23].
To find all the bifurcation diagrams existing next
to the singular point one constructs the universal un-
folding of g, which has the form

G(w,X,C) = g(w,A) + k acihi(w,X) (31)

where h is a set of basis functions (usually polynomials
in w and X) spanning a certain vector space and a is
a set of k parameters (k is equal in most cases to the
number of the qualities defining g minus 2). For

example, the universal unfolding of the winged cusp is

G = w3 + 2 + a + a2w + a 3wX = 0

The universal unfolding describes all the local
bifurcation diagrams that the function F(y,vp) = 0 has
next to the origin. Thus, all the bifurcation diagrams
can be found by a systematic perturbation (unfolding)
of all the a parameters of the universal unfolding.
Golubitsky and Schaeffer proved that the a space
can be divided into regions with qualitatively different
bifurcation diagrams by three types of surfaces. The
first, called the hysteresis variety is the set of
all oa satisfying.

G = G = G = 0
w ww


Eliminating w and X from these equations gives a
single algebraic equation defining a surface in the a-
space. When the parameters cross this variety a hys-
teresis loop typically appears or disappears (Fig. 6A).
The second surface called the isola variety is
the set of all a satisfying



FIGURE 6. Possible transitions of a local bifurcation dia-
gram (middle column) at the hysteresis (A) isola (B and
C) and the double limit (D and E) varieties into one of
two different forms [14].


b -

b c

Do = Vk(Tf)/q

FIGURE 7. Schematic bifurcation diagrams describing
the dependence of the conversion on the residence time
(Da) for a first order exothermic reaction [26].

G = G, = GX = 0 (34)

When a crosses this variety two limit points typically
appear or disappear and an isolated branch of solu-
tions appears or disappears if
A wG )2 aX 32 (35)
A = W-J 3W2 DX2

is negative (Fig. 6B) or the bifurcation diagram sepa-
rates into two isolated curves if A > 0 (Fig. 6C).
The third surface, called the double-limit variety,
is the set of a satisfying the four equations

g(w1,A,a) = g(w2,x,'3) = 2g (wiA,')

= (w 2,A,a) = 0
3W 2

w I w2 (36)

This variety can exist only for functions which
have at least four solutions for some values of the
bifurcation variable. When a crosses this variety the
relative position of two limit points changes (Figs. 6D
and 6E). This shift affects the type of branches which
are attained following an ignition or extinction. For
example, the transition between cases c and d in Fig.
2 requires crossing of this variety.
The first application of this technique to a chemi-
cally reacting system was presented by Golubitsky
and Keyfitz [25] who considered the dependence of
the conversion on the residence time in a CSTR in
which a single irreversible, first-order, exothermic

I - --- -


reaction occurs. They were able to show that there
exists in this case a one parameter family of winged
cusp singular points. Next to each singular point
seven different types of bifurcation diagrams exist,
shown schematically in Fig. 7. This is a very powerful
a priori prediction as all previous studies failed to pre-
dict the diagrams shown in cases e and g in the figure.
Many other problems were analyzed by Balakotaiah
[19, 26].
In practice it is often important to predict the
types of bifurcation diagrams which exist in the phys-
ical parameter space, not in the vicinity of the singular
point and the impact of a change in the parameters on
the bifurcation diagram. To answer this question we
need to divide the global parameter space into regions
having different bifurcation diagrams.
We shall explain first how this can be done for a
function F = 0 which is: (a) smooth with respect to y
and pL in the feasible region, (b) does not vanish on the
boundaries of the feasible y values and has no limit
point on a feasible [L boundary, and (c) has only sin-
gularities of finite codimension.
A change in the bifurcation diagram in such a case
can occur only when the parameters cross either the
hysteresis, isola or double-limit variety of the non-
linear function F = 0 (defined by Eqs. 33-36 with F
replacing G). This division of the physical parameter
space is very useful in many applications.
This scheme was used by Balakotaiah [27] to con-
struct the hysteresis and isola varieties for the model
describing the influence of the residence time on the
conversion in a cooled CSTR (a double limit variety
does not exist in this case). By analyzing the shape of
the cross sections of these varieties he was able to
show that the seven types of local bifurcation dia-
grams predicted by the local analysis of Golubitsky
and Keyfitz [25] (Fig. 7) are the only ones existing in
the global physical parameter space. Moreover, it was
possible to develop a very simple master map (Fig. 8)
which divides the T/Tf vs y space into regions having
different types of bifurcation diagrams. Inspection of
the map indicates that all the boundaries between the
various regions are given by very simple algebraic
relations. It indicates for example that diagrams with
an inverse S (types e and g in Fig. 7) can be obtained
only if the absolute coolant temperature is less than
0.66, the feed temperature. Previous researchers used
in their numerical simulations coolant temperatures
close to those of the feed and therefore failed to dis-
cover these two diagrams. Other applications were
presented in [26].
The technique may be also extended to cases in
which the function F is not smooth for all y values by
generalizing the definitions of the limit points and


y = E/RTf

FIGURE 8. A master map of regions having different
bifurcation diagrams for a first order reaction in a CSTR.
(Letters denote diagrams shown in Fig. 7) [26].

varieties to non smooth functions. Problems of this
type are encountered when the rate expression is not
smooth and several applications of this generalization
are presented in [15, 16, 19]. When the function F
vanishes on the feasible y boundaries or when it has
a limit point on a feasible R boundary a qualitative
change in the bifurcation diagram may occur even
when the parameters do not cross any of the three
variables. A method for handling these cases was pre-
sented in [18, 23].
The analysis indicates that the branching (bifurca-
tion) of solutions is an important methodology for
analyzing and characterizing the behavior of a non-
linear system. Hence, it is very useful to generate in
experimental studies a family of bifurcation diagrams
and not just a single diagram in order to find sys-
tematically all the interesting transitions. For exam-
ple, Fig. 9 shows a series of bifurcation diagrams ob-
tained by Xiou [28] during the co-oxidation of mix-
tures of hydrogen and ammonia in air. A branch of
extinguished solutions was found for all ammonia con-
centrations. The diagrams show a transition (bifurca-
tion) between a continuous ignited branch at 2 v. % H2
to a discontinuous ignited branch at 1.6 v.% H2. This
implies that an isola variety is crossed for some inter-
mediate hydrogen concentration. Moreover, the initial
decline in the wire temperature with increasing am-
monia concentration is indicative of kinetic interaction
between the two reactions. This qualitative informa-

tion is most useful in the development of candidate
kinetic rate expressions.
Experimentally observed limit (ignition and ex-
tinction) points should be used to construct a bifurca-
tion map, such as Fig. 3. This map shows regions with
different numbers of solutions and enables a rapid de-
tection of the various singular points. The defining
conditions of these points may be used to place con-
straints on candidate rate expressions [29]. A remain-
ing challenge is the use of the theory to predict the
minimal number of experiments needed to predict all
the possible multiplicity features and the selection of
the bifurcation variables which give the most dis-
criminating information. Moreover, the theory can
help solve the inverse problem, i.e., find the simplest
rate expression which can predict the observed mul-
tiplicity features [30].

The above discussion and examples show that
there exists at present an efficient algorithm for pre-
dicting the multiplicity features and structure of the
solutions of complex nonlinear problems. These
techiques enable one to replace the analysis of a highly
nonlinear model by the much simpler study of the fea-
tures of a normal form, and point out directly the simi-
lar features of nonlinear systems described by rather
different models. The ability of these techniques to
divide the global parameter space into regions with
different multiplicity features is very useful in many
This discussion was limited to steady-state multi-
plicity problems. However, similar techniques are

3 vol.% H2
2 5%
o ^2%
\ 400 1.0%

E No H2
D 1.6%-
* 200

0 1 2 3 4 5
NH3 Concentration (vol.%)

FIGURE 9. Bifurcation diagrams for the co-oxidation of
ammonia and hydrogen in air (Tg = 20) on a Pt wire.
An extinguished state exists all NH, concentrations [28].


available for predicting and classifying the dynamic
features of nonlinear systems [31]. These novel tools,
which are the subject of current research by
mathematicians, should enable the systematic solu-
tions of many important problems which are of in-
terest to chemical engineers. For example, Pismen
[32] and Lyberatos et. al. [33] have recently applied
some of these techniques to classify the dynamic be-
havior of a CSTR.
At present, we train our students by teaching the
analysis of linear or linearized systems, treating non-
linear systems as a special case. I believe that the
development of the new mathematical tools for hand-
ling nonlinear phenomena should enable us to change
the training of our students so that they can under-
stand and better predict the many nonlinear
phenomena which we encounter as chemical en-

I wish to thank my colleagues V. Balakotaiah, M.
Golubitsky, M. Harold, B. Keyfitz and M. Sheintuch
and my students R. Hu, J. P. Lee and G. Witmer for
many helpful discussions of these topics. I am in-
debted to the National Science Foundation for con-
tinued support of my research on this subject. Special
thanks are due to the 3M Company for support of this

a interfacial area per unit volume of reactor
bij elements of matrix b, defined by [12]
Ci concentration of species i
Cp specific heat capacity
Da Damk6hler number
E activation energy
f kinetic rate expression
F steady state algebraic equation
g normal form of singularity
G universal unfolding, defined by [31]
A H heat of reaction
h a set of basis functions
k codimension of singular point
K adsorption coefficient in Langmuir Hinshel-
wood rate expression
n reaction order
N number of reactions
p vector of parameters
q volumetric flow rate
q, sensitivity function, dy/dy(0)
R universal gas constant
T temperature

Tr reference temperature
U overall heat transfer coefficient
w state variable of normal form
x conversion
y state variable, dimensionless reactant con-
z length coordinate
a set of k parameters in the universal unfolding
P dimensionless temperature rise
-y dimensionless activation energy
,Ym minimum activation energy for which multip-
licity occurs
[L bifurcation variable
p density

c coolant conditions
f feed conditions
1 lower bound on variable or parameter
u upper bound on variable or parameter

1. Chen, Y. M., S. Rangachari and R. Jackson, "Theoretical and
Experimental Investigation of Fluid and Particle Flow in a
Verticle Standpipe," Ind. Eng. Chem. Fund. 23, 354, (1984).
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48, 571, (1928).
4. Davies, W., "Catalytic Combustion at High Temperatures,"
Phil. Mag., 17, 223, (1934).
5. Frank-Kamenetskii, D. A., "Calculation of Thermal Explosion
Limits," Acta Phys. Chim., URSS, 10, 365, (1939).
6. Zeldovich, Ya. B. and V. A. Zysin, "On the Theory of Thermal
combustion-Preformance of an Exothemic Reaction in a Jet,"
J. Tech. Phys., 11, 502, (1941).
7. Van Heerden, C., "Autothermic Processes, Properties and
Reactor Design," Ind. Eng. Chem., 45, 1242, (1953).
8. Bilous, 0., and N. R. Amundson, "Chemical Reactor Stability
and Sensitivity," AICHE J., 1, 513, (1955).
9. Aris, R., "On Stability Criteria of Chemical Reaction En-
gineering," Chem. Eng. Sci., 24, 149, (1969).
10. Chang, H. C., and J. M. Calo, "Exact Criteria for Uniqueness
and Multiplicity of an N-th Order Chemical Reaction via a
Catastrophe Theory Approach," Chem. Eng. Sci., 34, 285,
11. Tsotsis, T. T., and R. A. Schmitz, "Exact Uniqueness and
Multiplicity Criteria for a Positive Order Arrhenius Reaction
in a Lumped System," Chem. Eng. Sci., 34, 135, (1979).
12. Leib, R. M., and D. Luss, "Exact Uniqueness and Multiplicity
Criteria for an N-th Order Reaction in a CSTR," Chem. Eng.
Sci., 36, 210 (1981).
13. Harold, M. P., and D. Luss, "An Experimental Study of
Steady-State Multiplicity of Two Parallel Catalytic Reac-
tions," Chem. Eng. Sci., 40, 39, (1985).


14. Balakotaiah, V. and D. Luss, "Structure of the Steady-State
Solutions of Lumped Parameter Chemically Reacting Sys-
tems," Chem. Eng. Sci., 11, 1611, (1982).
15. Hu, R., V. Balakotaiah and D. Luss, "Multip;licity Features
of Porous Catalytic Pellets-I. Single Zeroth-Order Reaction
Case," Chem. Eng. Sci., 40, 589 (1985).
16. Hu, R., V. Balakotaiah and D. Luss, "Multiplicity Features of
Porous Catalytic Pellets II. Influence of Reaction Order and
Pellet Geometry," Chem. Eng. Sci., 40, 599, (1985).
17. Brocker, Th., and L. Lander, Differentiable Germs and Catas-
trophes, Cambridge University Press, (1975).
18. Balakotaiah V. and D. Luss, "Global Analysis of the Multipli-
city Features of Multi-Reaction Lumped Parameter Systems,"
Chem. Eng. Sci., 39, 865, (1984).
19. Balakotaiah, V. and D. Luss, "Steady-State Multiplicity Fea-
tures of Lumped Parameter Chemically Reacting Systems,"
in Dynamics of Nonlinear Systems. V. Hlavacek, ed., Gordon
and Breach Inc., (1986).
20. Balakotaiah, V., D. Luss and B. L. Keyfitz, "Steady-State
Multiplicity Analysis of Lumped Parameter Systems De-
scribed by a Set of Algebraic Equations," Chem. Eng. Comm.,
36, 121, (1985).
21. Witmer, G., V. Balakotaiah and D. Luss, "Multiplicity Fea-
tures of Distributed Systems, Langmuir-Hinshelwood Reac-
tion in a Porous Catalyst," Chem. Eng. Sci., 41, (1986) to be
22. Balakotaiah, V., and D. Luss, "Input-Multiplicity in Lumped
Parameter Systems," Chem. Eng. Comm. (1986) to be pub-
23. Golubitsky, M. and D. G. Schaeffer, Singularity and Groups
in Bifurcation Theory, Volume 1, Springer Verlag, N. Y.,
24. Golubitsky, M. and D. Schaeffer, "A Theory for Imperfect
Bifurcation Via Singularity Theory," Comm. Pure Appl. Mth.,
32, 21, (1979).
25. Golubitsky, M. and B. L. Keyfitz, "A Qualitative Study of the
Steady-State Solutions for a Continuous Flow Stirred Tank
Chemical Reactor," SIAM J. Math Anal., 11, 316, (1980).
26. Balakotaiah, V., and D. Luss, "Multiplicity Features of React-
ing Systems-Dependence of the Steady-States of a CSTR on
the Residence Time," Chem. Eng. Sci., 38, 1709, (1983).
27. Balakotaiah, V., and D. Luss, "Analysis of the Multiplicity
Patterns of a CSTR," Chem. Eng. Comm., 13, 111, (1981); 19,
185, (1982).
28. Xiou, R. R., M. Sheintuch and D. Luss, "Experimental Study
of Bifurcation Diagrams and Maps of Two Parallel Interacting
Catalytic Reactions," Chem. Eng. Sci., 41 (1986) to be pub-
29. Sheintuch, M. and D. Luss, "Application of Singularity Theory
to Modeling of Steady State Multiplicity: Propylene Oxidation
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Continued from page 31.
mance, and a critique of a process control system. This
activity is part of a second-semester senior course.
Previously, the students have taken the unit opera-
tions courses, the process control course, and most
have had a laboratory in piping layout. Details of the
latter are given elsewhere [4]. Blueprints and operat-
ing data for the plant are both needed and available.


We have been using the boiler house since 1970,
although in the early days we used it primarily as a
tour so that students could get used to what processes
looked like. Being on campus, we did not encounter
the usual worries associated with plant tours, such as
arranging for transportation, not getting the type of
tour our students needed at that time in their develop-
ment, or causing embarrassment because the students
did not really know what was going on. The early
positive response of the students, coupled with the
generous cooperation by the boiler house personnel,
led us to integrate boiler house activities more and
more into our program. We have approached our use
of the boiler house as though it were an on-site, large
scale laboratory facility that could be used to develop
students practical knowhow and confidence in tackling
real, professional problems.
The boiler house project for seniors has been part
of our program since about 1974 and has been rated
very highly by the students. The computer simulation
activity started in 1984 and, although it's too early to
see the full impact, we have noticed already that they
are working on the senior design project and are
showing a maturity, a professionalism, and an intui-
tion about processes that is rewarding.

We are pleased to acknowledge the outstanding
cooperation and assistance we have received from the
boiler house personnel. They take pride in their work,
maintain one of the cleanest plants we have seen, and
have made visits to their plant a real treat.


1. Wood, P. E. (1984), "An Introduction to Steady-State Simula-
tion and Design," McMaster University, HamiltQn, Ontario.
2. Woods, D. R. et al. (1978), "The Travelling Circus as a Means
of Introducing Practical Hardware," Chem. Eng. Ed., Sum-
mer, p. 116 to 117.
3. Dunn, R. W. et al. (1981), "Touching Technology," Chem.
Tech., p. 586 to 587.
4. Woods, D. R. and R. W. Dunn, (1979), "Piping Layout as a
Laboratory Project," Chem. Eng. Ed., Spring, p. 64-68. l



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